Question

g.co.c.9 worksheet #1
name:

1. solve the following.

a) x =
y =
b) x =
y =
c) x =
y =

1. ∠5 and ∠3 are vertical angles. t or f
2. ∠1 and ∠5 are a linear pair. t or f
3. ∠4 and ∠3 are adjacent angles. t or f
4. ∠4 and ∠1 are vertical angles. t or f
5. ∠3 and ∠4 are a linear pair. t or f
6. if ∠a and ∠b are supplements and m∠a = 150°, what is m∠b?
7. if ∠a and ∠b are complements and m∠a = 27°, what is m∠b?
8. if ∠a and ∠b are vertical angles and m∠a = 36°, what is m∠b?
9. if ∠a and ∠b are a linear pair and m∠a = 2x + 8 and m∠b = 3x + 2, what is the value of x? x =
10. if ∠a and ∠b are vertical angles and m∠a = 7x - 5 and m∠b = 4x + 10, what is the value of x? x =
11. provide the name of the following relationships.

a) ∠1 & ∠6
b) ∠2 & ∠7
c) ∠16 & ∠14
d) ∠14 & ∠11
e) ∠1 & ∠7
f) ∠6 & ∠5
g) ∠15 & ∠10
h) ∠18 & ∠2
i) ∠13 & ∠12
j) ∠16 & ∠9

1. find the measure of the angle and give a reason for knowing it.

a) m∠1 = (reason)
b) m∠2 = (reason)
c) m∠3 = (reason)
d) m∠4 = (reason)
e) m∠5 = (reason)

1. find the measure of the angle.

a) m∠1 =
b) m∠2 =
c) m∠3 =
d) m∠4 =
e) m∠5 =
f) m∠6 =

Explanation:

Step1: Solve 1a (vertical/linear pairs)

Vertical angles are equal; linear pairs sum to $180^\circ$.

• a) $x = 67^\circ$ (vertical to $67^\circ$), $y = 180^\circ - 67^\circ = 113^\circ$
• b) $3x-5 = 127^\circ$ → $3x=132$ → $x=44$; $y = 180^\circ - 127^\circ = 53^\circ$
• c) $5x-15 = 90^\circ$ → $5x=105$ → $x=21$; $y=90^\circ$ (vertical to right angle)

Step2: True/False (2-6)

Vertical angles are opposite; linear pairs sum to $180^\circ$; adjacent angles share a side.

• 2. T (vertical angles)
• 3. T (linear pair)
• 4. T (adjacent angles)
• 5. T (vertical angles)
• 6. T (linear pair)

Step3: Solve supplementary angles (7)

Supplementary angles sum to $180^\circ$.
$m\angle B = 180^\circ - 150^\circ = 30^\circ$

Step4: Solve complementary angles (8)

Complementary angles sum to $90^\circ$.
$m\angle B = 90^\circ - 27^\circ = 63^\circ$

Step5: Solve vertical angles (9)

Vertical angles are equal.
$m\angle B = 36^\circ$

Step6: Solve linear pair (10)

Linear pairs sum to $180^\circ$.
$2x+8 + 3x+2 = 180$ → $5x+10=180$ → $5x=170$ → $x=34$

Step7: Solve vertical angles (11)

Vertical angles are equal.
$7x-5 = 4x+10$ → $3x=15$ → $x=5$

Step8: Angle relationships (12)

Identify angle pair names:

• a) Corresponding angles
• b) Alternate interior angles
• c) Alternate exterior angles
• d) Same-side interior angles
• e) Vertical angles
• f) Linear pair
• g) Alternate exterior angles
• h) Linear pair
• i) Same-side interior angles
• j) Corresponding angles

Step9: Find angles (13)

Use vertical/linear pair properties:

• a) $m\angle1=110^\circ$ (vertical to $110^\circ$)
• b) $m\angle2=70^\circ$ (linear pair with $\angle1$)
• c) $m\angle3=70^\circ$ (vertical to $\angle2$)
• d) $m\angle4=70^\circ$ (corresponding to $\angle3$)
• e) $m\angle5=70^\circ$ (vertical to $\angle4$)

Step10: Find angles (14)

Use vertical/linear/corresponding angles:

• a) $m\angle1=83^\circ$ (corresponding to $83^\circ$)
• b) $m\angle2=97^\circ$ (linear pair with $\angle1$)
• c) $m\angle3=83^\circ$ (vertical to $\angle1$)
• d) $m\angle4=97^\circ$ (vertical to $\angle2$)
• e) $m\angle5=97^\circ$ (corresponding to $\angle4$)
• f) $m\angle6=97^\circ$ (linear pair with $83^\circ$)

Answer:

1.
a) $x=67^\circ$, $y=113^\circ$
b) $x=44$, $y=53^\circ$
c) $x=21$, $y=90^\circ$

1. T
2. T
3. T
4. T
5. T
6. $30^\circ$
7. $63^\circ$
8. $36^\circ$
9. $x=34$
10. $x=5$

12.
a) Corresponding angles
b) Alternate interior angles
c) Alternate exterior angles
d) Same-side interior angles
e) Vertical angles
f) Linear pair
g) Alternate exterior angles
h) Linear pair
i) Same-side interior angles
j) Corresponding angles
13.
a) $110^\circ$ (vertical angles are equal)
b) $70^\circ$ (linear pair sums to $180^\circ$)
c) $70^\circ$ (vertical angles are equal)
d) $70^\circ$ (corresponding angles are equal)
e) $70^\circ$ (vertical angles are equal)
14.
a) $83^\circ$
b) $97^\circ$
c) $83^\circ$
d) $97^\circ$
e) $97^\circ$
f) $97^\circ$