Question

in the figure, line e || line f. which statement is true?
options:
○ ( mangle 6 = 70^circ )
○ ( mangle 3 = 70^circ )
○ line ( f perp ) line ( g )
○ ( angle 2 cong angle 7 )

Explanation:

Step1: Analyze ∠6

∠6 and the 110° angle are vertical angles? No, wait, ∠6 and the 110° angle: actually, ∠5 and 110° are supplementary? Wait, no, ∠5 and 110° are adjacent and form a linear pair? Wait, line g intersects line f, so the angle adjacent to 110° (∠5) and 110° are supplementary. Wait, no, ∠5 and 110°: actually, ∠6 is vertical to the angle adjacent? Wait, maybe better to look at ∠3. Since line e || line f, and line g is a transversal? Wait, no, line g is a transversal for lines e and f? Wait, line e and f are parallel, line g is a transversal? Wait, no, the intersection: line e and line g intersect at a point, line f and line g intersect at another point. So line g is a transversal for lines e and f. Now, ∠3: let's see, ∠4 and the 110° angle: since e || f, ∠4 should be equal to the angle adjacent to 110°? Wait, maybe first, the 110° angle and ∠5: they are adjacent, so ∠5 + 110° = 180°, so ∠5 = 70°? Wait, no, ∠5 and 110°: are they vertical? No, ∠5 and the angle opposite to 110°? Wait, the intersection of line f and g: the angles around that point. So the 110° angle and ∠5 are adjacent, forming a linear pair, so ∠5 = 180° - 110° = 70°? Wait, no, ∠5 and 110°: if they are adjacent, then yes, linear pair. Then, since e || f, ∠4 = ∠5 (alternate interior angles)? Wait, ∠4 and ∠5: are they alternate interior angles? Line e and f are parallel, transversal is line g? Wait, line g is a transversal, so ∠4 and ∠5 are alternate interior angles, so ∠4 = ∠5. Then ∠4 and ∠3: vertical angles? No, ∠4 and ∠3: adjacent, linear pair? Wait, ∠4 and ∠3: when line e and the other line (the one with ∠1, ∠2, ∠3, ∠4) intersect, ∠4 and ∠3 are adjacent, forming a linear pair? Wait, no, ∠1, ∠2, ∠3, ∠4: around the intersection of line e and the horizontal line (line g? Wait, maybe the horizontal line is line g. So line g is horizontal, line e and f are parallel, slanting lines. So ∠3: let's see, ∠4 and ∠3: are they vertical angles? No, ∠1 and ∠3 are vertical angles, ∠2 and ∠4 are vertical angles. Wait, maybe I made a mistake. Let's re-examine.

Wait, the 110° angle is at the intersection of line f and g. So the angle opposite to 110° is ∠7, which is equal to 110° (vertical angles). Then ∠6 is adjacent to 110°, so ∠6 = 180° - 110° = 70°? Wait, no, ∠6 and 110°: are they adjacent? Let's see the diagram: the intersection of f and g has angles: 110°, ∠5, ∠6, ∠7. So 110° and ∠5 are adjacent (linear pair), so ∠5 = 70°; ∠5 and ∠6 are adjacent (linear pair), so ∠6 = 110°? No, that can't be. Wait, maybe the 110° angle and ∠6 are vertical angles? No, vertical angles are opposite. So 110° and ∠6: if they are opposite, then ∠6 = 110°, but that's not one of the options. Wait, the options are m∠6=70°, m∠3=70°, line f ⊥ line g, ∠2 ≅ ∠7.

Wait, let's consider line e || line f, and the transversal is the line that intersects both e and f (the one with ∠1, ∠2, ∠3, ∠4 and ∠5, ∠6, ∠7). So ∠3 and ∠5: are they corresponding angles? Since e || f, corresponding angles are equal. ∠5 is 70° (since 180° - 110° = 70°), so ∠3 = ∠5 = 70°? Wait, that would make m∠3=70° true. Let's check other options:

- m∠6=70°: ∠6 is adjacent to 110°, so if 110° and ∠6 are linear pair, then ∠6=70°? Wait, no, 110° + ∠6 = 180°? If they are adjacent, then yes. Wait, maybe I confused the angles. Let's look at the intersection of f and g: the angle given is 110°, so the angle adjacent to it (∠5) is 70° (180-110), then ∠6 is vertical to 110°? No, vertical angles are equal. So 110° and ∠6: if they are vertical, then ∠6=110°, but that's not an option. Wait, maybe the angle labeled 110° and ∠6 are supplementary? No, that would be 70°, but maybe ∠6 is equal to ∠5? Wait, ∠5 and ∠6: are they vertical? No, ∠5 and ∠7 are vertical, ∠6 and 110° are vertical. So ∠6=110°, so m∠6=70° is false.

- line f ⊥ line g: the angle is 110°, not 90°, so false.

- ∠2 ≅ ∠7: ∠2 and ∠7. ∠2 is vertical to ∠4, ∠7 is 110° (vertical to 110°), so ∠2 would be equal to ∠4, which is equal to ∠5 (70°), so ∠2=70°, ∠7=110°, so not congruent.

- m∠3=70°: ∠3 and ∠5 are corresponding angles (since e || f, transversal is the line intersecting them), so ∠3=∠5=70°, so this is true.

Wait, maybe my initial analysis of ∠5 was wrong. Let's re-express:

At the intersection of line f and line g, the angles are: 110°, ∠5, ∠6, ∠7.

- 110° and ∠5 are adjacent (linear pair), so 110° + ∠5 = 180° ⇒ ∠5 = 70°.

- ∠5 and ∠6 are adjacent (linear pair), so ∠5 + ∠6 = 180° ⇒ ∠6 = 110°.

- ∠6 and ∠7 are adjacent (linear pair), so ∠6 + ∠7 = 180° ⇒ ∠7 = 70°? Wait, no, that can't be. Wait, vertical angles: 110° and ∠6 are vertical? No, vertical angles are opposite. So 110° and ∠6: if they are opposite, then ∠6=110°, and ∠5 and ∠7 are vertical, so ∠5=∠7. So 110° + ∠5 = 180° ⇒ ∠5=70°, so ∠7=70°.

Now, line e || line f, and the transversal is the line that intersects both (the one with ∠1, ∠2, ∠3, ∠4). So ∠3 and ∠7: are they corresponding angles? Wait, ∠3 and ∠7: let's see, ∠3 is at the intersection of line e and the transversal, ∠7 is at the intersection of line f and the transversal. If e || f, then corresponding angles are equal. So ∠3=∠7=70°, so m∠3=70° is true.

Yes, that makes sense. So the correct statement is m∠3=70°.

Step2: Verify other options

- m∠6=70°: ∠6 is 110° (vertical to 110°), so false.
- line f ⊥ line g: angle is 110°, not 90°, false.
- ∠2 ≅ ∠7: ∠2 is vertical to ∠4, which is equal to ∠5=70°, so ∠2=70°; ∠7=70°? Wait, no, earlier I thought ∠7=70°, but if ∠7 is vertical to ∠5, then ∠7=70°, so ∠2=70° and ∠7=70°, so ∠2≅∠7? Wait, now I'm confused. Wait, let's re-express all angles:

At intersection of f and g:

- 110° (given)
- ∠5: adjacent to 110°, so 180-110=70°
- ∠6: vertical to 110°, so 110°
- ∠7: vertical to ∠5, so 70°

At intersection of e and the transversal (same as f's transversal):

- ∠1: vertical to ∠3
- ∠2: vertical to ∠4
- ∠3: corresponding to ∠7 (since e || f), so ∠3=∠7=70°
- ∠4: corresponding to ∠5 (since e || f), so ∠4=∠5=70°
- So ∠2=∠4=70°, ∠7=70°, so ∠2≅∠7? Wait, that would mean both m∠3=70° and ∠2≅∠7 are true? But that can't be. Wait, maybe the diagram is different. Wait, the options are:

1. m∠6=70°: ∠6 is 110°, so false.

2. m∠3=70°: ∠3=70°, true.

3. line f ⊥ line g: angle is 110°, not 90°, false.

4. ∠2 ≅ ∠7: ∠2=70°, ∠7=70°, so they are congruent? Wait, but that would mean two options are true, which is impossible. So I must have made a mistake.

Wait, maybe ∠2 and ∠7: ∠2 is at the intersection of e and the transversal, ∠7 is at f and g. Are they corresponding? No, maybe alternate interior? Wait, line e || f, transversal is the line connecting the two intersections (the one with ∠1-∠4 and ∠5-∠7). So ∠2 and ∠7: are they alternate interior angles? Let's see: ∠2 is on line e, below the transversal; ∠7 is on line f, below the transversal? No, maybe not. Wait, maybe the diagram has line e and f as parallel, and the transversal is the line with ∠1-∠4, and line g is another transversal. Wait, the problem says "line e || line f", so the two parallel lines are e and f, and line g is a transversal? No, line g intersects both e and f, so line g is the transversal. So ∠3 and ∠7: corresponding angles (same position relative to e, f, and g), so ∠3=∠7. ∠7 is 70° (since ∠7 is vertical to ∠5, which is 70°), so ∠3=70°, so m∠3=70° is true.

∠2 and ∠7: ∠2 is vertical to ∠4, which is equal to ∠5=70°, so ∠2=70°, ∠7=70°, so ∠2≅∠7? But that would mean both options 2 and 4 are true, which is not possible. So maybe my analysis of ∠7 is wrong. Wait, the 110° angle: is it adjacent to ∠7? No, ∠7 is opposite to ∠5? Wait, no, at the intersection of f and g, the angles are:

- Top: 110°

- Right: ∠7

- Bottom: ∠6

- Left: ∠5

So 110° and ∠5 are adjacent (linear pair), so 110 + ∠5 = 180 ⇒ ∠5=70°

∠5 and ∠6 are adjacent (linear pair), so ∠5 + ∠6 = 180 ⇒ ∠6=110°

∠6 and ∠7 are adjacent (linear pair), so ∠6 + ∠7 = 180 ⇒ ∠7=70°

∠7 and 110° are adjacent (linear pair), so ∠7 + 110 = 180 ⇒ ∠7=70°, which matches.

Now, at the intersection of e and g:

- ∠1: top left

- ∠4: top right

- ∠3: bottom right

- ∠2: bottom left

So ∠4 and ∠5: alternate interior angles (since e || f, g is transversal), so ∠4=∠5=70°

∠3 and ∠4: linear pair, so ∠3 + ∠4 = 180 ⇒ ∠3=110°? Wait, that's the mistake! Oh no, I messed up the linear pair. ∠3 and ∠4 are adjacent, forming a linear pair, so ∠3 + ∠4 = 180°. Since ∠4=70° (alternate interior with ∠5), then ∠3=180-70=110°. Oh! That's the error. So my earlier analysis was wrong.

So let's correct:

At intersection of f and g:

- 110° (top)

- ∠5: left, 180-110=70° (linear pair with 110°)

- ∠6: bottom, vertical to 110°, so 110° (vertical angles are equal)

- ∠7: right, vertical to ∠5, so 70° (vertical angles are equal)

At intersection of e and g:

- ∠1: top left, vertical to ∠3 (bottom right)

- ∠4: top right, alternate interior with ∠5 (left at f and g), so ∠4=∠5=70° (since e || f, alternate interior angles are equal)

- ∠3: bottom right, linear pair with ∠4, so ∠3=180-∠4=180-70=110°

- ∠2: bottom left, vertical to ∠4, so ∠2=∠4=70°

Now, let's check the options:

1. m∠6=70°: ∠6=110°, so false.

2. m∠3=70°: ∠3=110°, so false.

3. line f ⊥ line g: angle is 110°, not 90°, so false.

4. ∠2 ≅ ∠7: ∠2=70°, ∠7=70°, so they are congruent (≅). So this is true.

Wait, now I see the mistake. Earlier, I thought ∠3 and ∠7 are corresponding, but actually, ∠3 is at e and g, ∠7 is at f and g. The transversal is g, so corresponding angles would be ∠1 and 110°, ∠4 and ∠5, ∠3 and ∠6, ∠2 and ∠7. Ah! Yes, ∠2 and ∠7 are corresponding angles (same position: bottom left at e and g, bottom right? No, wait, ∠2 is bottom left, ∠7 is bottom right? No, maybe alternate interior. Wait, ∠2 is on line e, below g, left side; ∠7 is on line f, below g, right side? No, maybe alternate exterior. Wait, no, let's use the correct corresponding angles.

When two parallel lines are cut by a transversal, corresponding angles are equal. So:

- ∠1 (top left at e and g) corresponds to 110° (top left at f and g) ⇒ ∠1=110°

- ∠4 (top right at e and g) corresponds to ∠5 (top right at f and g) ⇒ ∠4=∠5=70°

- ∠3 (bottom right at e and g) corresponds to ∠6 (bottom right at f and g) ⇒ ∠3=∠6=110°

- ∠2 (bottom left at e and g) corresponds to ∠7 (

Answer:

Step1: Analyze ∠6

∠6 and the 110° angle are vertical angles? No, wait, ∠6 and the 110° angle: actually, ∠5 and 110° are supplementary? Wait, no, ∠5 and 110° are adjacent and form a linear pair? Wait, line g intersects line f, so the angle adjacent to 110° (∠5) and 110° are supplementary. Wait, no, ∠5 and 110°: actually, ∠6 is vertical to the angle adjacent? Wait, maybe better to look at ∠3. Since line e || line f, and line g is a transversal? Wait, no, line g is a transversal for lines e and f? Wait, line e and f are parallel, line g is a transversal? Wait, no, the intersection: line e and line g intersect at a point, line f and line g intersect at another point. So line g is a transversal for lines e and f. Now, ∠3: let's see, ∠4 and the 110° angle: since e || f, ∠4 should be equal to the angle adjacent to 110°? Wait, maybe first, the 110° angle and ∠5: they are adjacent, so ∠5 + 110° = 180°, so ∠5 = 70°? Wait, no, ∠5 and 110°: are they vertical? No, ∠5 and the angle opposite to 110°? Wait, the intersection of line f and g: the angles around that point. So the 110° angle and ∠5 are adjacent, forming a linear pair, so ∠5 = 180° - 110° = 70°? Wait, no, ∠5 and 110°: if they are adjacent, then yes, linear pair. Then, since e || f, ∠4 = ∠5 (alternate interior angles)? Wait, ∠4 and ∠5: are they alternate interior angles? Line e and f are parallel, transversal is line g? Wait, line g is a transversal, so ∠4 and ∠5 are alternate interior angles, so ∠4 = ∠5. Then ∠4 and ∠3: vertical angles? No, ∠4 and ∠3: adjacent, linear pair? Wait, ∠4 and ∠3: when line e and the other line (the one with ∠1, ∠2, ∠3, ∠4) intersect, ∠4 and ∠3 are adjacent, forming a linear pair? Wait, no, ∠1, ∠2, ∠3, ∠4: around the intersection of line e and the horizontal line (line g? Wait, maybe the horizontal line is line g. So line g is horizontal, line e and f are parallel, slanting lines. So ∠3: let's see, ∠4 and ∠3: are they vertical angles? No, ∠1 and ∠3 are vertical angles, ∠2 and ∠4 are vertical angles. Wait, maybe I made a mistake. Let's re-examine.

Wait, the 110° angle is at the intersection of line f and g. So the angle opposite to 110° is ∠7, which is equal to 110° (vertical angles). Then ∠6 is adjacent to 110°, so ∠6 = 180° - 110° = 70°? Wait, no, ∠6 and 110°: are they adjacent? Let's see the diagram: the intersection of f and g has angles: 110°, ∠5, ∠6, ∠7. So 110° and ∠5 are adjacent (linear pair), so ∠5 = 70°; ∠5 and ∠6 are adjacent (linear pair), so ∠6 = 110°? No, that can't be. Wait, maybe the 110° angle and ∠6 are vertical angles? No, vertical angles are opposite. So 110° and ∠6: if they are opposite, then ∠6 = 110°, but that's not one of the options. Wait, the options are m∠6=70°, m∠3=70°, line f ⊥ line g, ∠2 ≅ ∠7.

Wait, let's consider line e || line f, and the transversal is the line that intersects both e and f (the one with ∠1, ∠2, ∠3, ∠4 and ∠5, ∠6, ∠7). So ∠3 and ∠5: are they corresponding angles? Since e || f, corresponding angles are equal. ∠5 is 70° (since 180° - 110° = 70°), so ∠3 = ∠5 = 70°? Wait, that would make m∠3=70° true. Let's check other options:

• m∠6=70°: ∠6 is adjacent to 110°, so if 110° and ∠6 are linear pair, then ∠6=70°? Wait, no, 110° + ∠6 = 180°? If they are adjacent, then yes. Wait, maybe I confused the angles. Let's look at the intersection of f and g: the angle given is 110°, so the angle adjacent to it (∠5) is 70° (180-110), then ∠6 is vertical to 110°? No, vertical angles are equal. So 110° and ∠6: if they are vertical, then ∠6=110°, but that's not an option. Wait, maybe the angle labeled 110° and ∠6 are supplementary? No, that would be 70°, but maybe ∠6 is equal to ∠5? Wait, ∠5 and ∠6: are they vertical? No, ∠5 and ∠7 are vertical, ∠6 and 110° are vertical. So ∠6=110°, so m∠6=70° is false.

• line f ⊥ line g: the angle is 110°, not 90°, so false.

• ∠2 ≅ ∠7: ∠2 and ∠7. ∠2 is vertical to ∠4, ∠7 is 110° (vertical to 110°), so ∠2 would be equal to ∠4, which is equal to ∠5 (70°), so ∠2=70°, ∠7=110°, so not congruent.

• m∠3=70°: ∠3 and ∠5 are corresponding angles (since e || f, transversal is the line intersecting them), so ∠3=∠5=70°, so this is true.

Wait, maybe my initial analysis of ∠5 was wrong. Let's re-express:

At the intersection of line f and line g, the angles are: 110°, ∠5, ∠6, ∠7.

• 110° and ∠5 are adjacent (linear pair), so 110° + ∠5 = 180° ⇒ ∠5 = 70°.

• ∠5 and ∠6 are adjacent (linear pair), so ∠5 + ∠6 = 180° ⇒ ∠6 = 110°.

• ∠6 and ∠7 are adjacent (linear pair), so ∠6 + ∠7 = 180° ⇒ ∠7 = 70°? Wait, no, that can't be. Wait, vertical angles: 110° and ∠6 are vertical? No, vertical angles are opposite. So 110° and ∠6: if they are opposite, then ∠6=110°, and ∠5 and ∠7 are vertical, so ∠5=∠7. So 110° + ∠5 = 180° ⇒ ∠5=70°, so ∠7=70°.

Now, line e || line f, and the transversal is the line that intersects both (the one with ∠1, ∠2, ∠3, ∠4). So ∠3 and ∠7: are they corresponding angles? Wait, ∠3 and ∠7: let's see, ∠3 is at the intersection of line e and the transversal, ∠7 is at the intersection of line f and the transversal. If e || f, then corresponding angles are equal. So ∠3=∠7=70°, so m∠3=70° is true.

Yes, that makes sense. So the correct statement is m∠3=70°.

Step2: Verify other options

• m∠6=70°: ∠6 is 110° (vertical to 110°), so false.
• line f ⊥ line g: angle is 110°, not 90°, false.
• ∠2 ≅ ∠7: ∠2 is vertical to ∠4, which is equal to ∠5=70°, so ∠2=70°; ∠7=70°? Wait, no, earlier I thought ∠7=70°, but if ∠7 is vertical to ∠5, then ∠7=70°, so ∠2=70° and ∠7=70°, so ∠2≅∠7? Wait, now I'm confused. Wait, let's re-express all angles:

At intersection of f and g:

• 110° (given)
• ∠5: adjacent to 110°, so 180-110=70°
• ∠6: vertical to 110°, so 110°
• ∠7: vertical to ∠5, so 70°

At intersection of e and the transversal (same as f's transversal):

• ∠1: vertical to ∠3
• ∠2: vertical to ∠4
• ∠3: corresponding to ∠7 (since e || f), so ∠3=∠7=70°
• ∠4: corresponding to ∠5 (since e || f), so ∠4=∠5=70°
• So ∠2=∠4=70°, ∠7=70°, so ∠2≅∠7? Wait, that would mean both m∠3=70° and ∠2≅∠7 are true? But that can't be. Wait, maybe the diagram is different. Wait, the options are:

1. m∠6=70°: ∠6 is 110°, so false.

1. m∠3=70°: ∠3=70°, true.

1. line f ⊥ line g: angle is 110°, not 90°, false.

1. ∠2 ≅ ∠7: ∠2=70°, ∠7=70°, so they are congruent? Wait, but that would mean two options are true, which is impossible. So I must have made a mistake.

Wait, maybe ∠2 and ∠7: ∠2 is at the intersection of e and the transversal, ∠7 is at f and g. Are they corresponding? No, maybe alternate interior? Wait, line e || f, transversal is the line connecting the two intersections (the one with ∠1-∠4 and ∠5-∠7). So ∠2 and ∠7: are they alternate interior angles? Let's see: ∠2 is on line e, below the transversal; ∠7 is on line f, below the transversal? No, maybe not. Wait, maybe the diagram has line e and f as parallel, and the transversal is the line with ∠1-∠4, and line g is another transversal. Wait, the problem says "line e || line f", so the two parallel lines are e and f, and line g is a transversal? No, line g intersects both e and f, so line g is the transversal. So ∠3 and ∠7: corresponding angles (same position relative to e, f, and g), so ∠3=∠7. ∠7 is 70° (since ∠7 is vertical to ∠5, which is 70°), so ∠3=70°, so m∠3=70° is true.

∠2 and ∠7: ∠2 is vertical to ∠4, which is equal to ∠5=70°, so ∠2=70°, ∠7=70°, so ∠2≅∠7? But that would mean both options 2 and 4 are true, which is not possible. So maybe my analysis of ∠7 is wrong. Wait, the 110° angle: is it adjacent to ∠7? No, ∠7 is opposite to ∠5? Wait, no, at the intersection of f and g, the angles are:

• Top: 110°

• Right: ∠7

• Bottom: ∠6

• Left: ∠5

So 110° and ∠5 are adjacent (linear pair), so 110 + ∠5 = 180 ⇒ ∠5=70°

∠5 and ∠6 are adjacent (linear pair), so ∠5 + ∠6 = 180 ⇒ ∠6=110°

∠6 and ∠7 are adjacent (linear pair), so ∠6 + ∠7 = 180 ⇒ ∠7=70°

∠7 and 110° are adjacent (linear pair), so ∠7 + 110 = 180 ⇒ ∠7=70°, which matches.

Now, at the intersection of e and g:

• ∠1: top left

• ∠4: top right

• ∠3: bottom right

• ∠2: bottom left

So ∠4 and ∠5: alternate interior angles (since e || f, g is transversal), so ∠4=∠5=70°

∠3 and ∠4: linear pair, so ∠3 + ∠4 = 180 ⇒ ∠3=110°? Wait, that's the mistake! Oh no, I messed up the linear pair. ∠3 and ∠4 are adjacent, forming a linear pair, so ∠3 + ∠4 = 180°. Since ∠4=70° (alternate interior with ∠5), then ∠3=180-70=110°. Oh! That's the error. So my earlier analysis was wrong.

So let's correct:

At intersection of f and g:

• 110° (top)

• ∠5: left, 180-110=70° (linear pair with 110°)

• ∠6: bottom, vertical to 110°, so 110° (vertical angles are equal)

• ∠7: right, vertical to ∠5, so 70° (vertical angles are equal)

At intersection of e and g:

• ∠1: top left, vertical to ∠3 (bottom right)

• ∠4: top right, alternate interior with ∠5 (left at f and g), so ∠4=∠5=70° (since e || f, alternate interior angles are equal)

• ∠3: bottom right, linear pair with ∠4, so ∠3=180-∠4=180-70=110°

• ∠2: bottom left, vertical to ∠4, so ∠2=∠4=70°

Now, let's check the options:

1. m∠6=70°: ∠6=110°, so false.

1. m∠3=70°: ∠3=110°, so false.

1. line f ⊥ line g: angle is 110°, not 90°, so false.

1. ∠2 ≅ ∠7: ∠2=70°, ∠7=70°, so they are congruent (≅). So this is true.

Wait, now I see the mistake. Earlier, I thought ∠3 and ∠7 are corresponding, but actually, ∠3 is at e and g, ∠7 is at f and g. The transversal is g, so corresponding angles would be ∠1 and 110°, ∠4 and ∠5, ∠3 and ∠6, ∠2 and ∠7. Ah! Yes, ∠2 and ∠7 are corresponding angles (same position: bottom left at e and g, bottom right? No, wait, ∠2 is bottom left, ∠7 is bottom right? No, maybe alternate interior. Wait, ∠2 is on line e, below g, left side; ∠7 is on line f, below g, right side? No, maybe alternate exterior. Wait, no, let's use the correct corresponding angles.

When two parallel lines are cut by a transversal, corresponding angles are equal. So:

• ∠1 (top left at e and g) corresponds to 110° (top left at f and g) ⇒ ∠1=110°

• ∠4 (top right at e and g) corresponds to ∠5 (top right at f and g) ⇒ ∠4=∠5=70°

• ∠3 (bottom right at e and g) corresponds to ∠6 (bottom right at f and g) ⇒ ∠3=∠6=110°

• ∠2 (bottom left at e and g) corresponds to ∠7 (