Question

angles challenge 2
recording sheet
name
write the measure of each angle.
angle 1 = __ angle 24 = _ angle 48 = __
angle 2 = __ angle 25 = _ angle 49 = __
angle 3 = __ angle 26 = _ angle 50 = __
angle 4 = __ angle 27 = _ angle 51 = __
angle 5 = __ angle 28 = _ angle 52 = __
angle 6 = __ angle 29 = _ angle 53 = __
angle 7 = __ angle 30 = _ angle 54 = __
angle 8 = __ angle 31 = _ angle 55 = __
angle 9 = __ angle 32 = _ angle 56 = __
angle 10 = __ angle 33 = _ angle 57 = __
angle 11 = __ angle 34 = _ angle 58 = __
angle 12 = __ angle 35 = _ angle 59 = __
angle 13 = __ angle 36 = _ angle 60 = __
angle 14 = 126 angle 37 = ___ angle 61 = __
angle 15 = __ angle 38 = _ angle 62 = __
angle 16 = __ angle 39 = _ angle 63 = __
angle 17 = __ angle 40 = _ angle 64 = __
angle 18 = __ angle 41 = _ angle 65 = __
angle 19 = __ angle 42 = _ angle 66 = __
angle 20 = __ angle 43 = _ angle 67 = __
angle 21 = __ angle 44 = _ angle 68 = __
angle 22 = __ angle 45 = _ angle 69 = __
angle 23 = __ angle 46 = _ angle 70 = __
angle 47 = ___ angle 71 = __
angles challenge 2
name
lines a and b are parallel. lines c and d are parallel. lines e and f are parallel. find
the missing angles. angles are not drawn to scale.

Answer:

To solve for the missing angles, we use properties of parallel lines (corresponding angles, alternate interior angles, supplementary angles, vertical angles). Let's start with a few examples:

Step 1: Angle 1 (supplementary to 109°)

Angles on a straight line sum to \( 180^\circ \).
\( \text{Angle } 1 = 180^\circ - 109^\circ = 71^\circ \)

Step 2: Angle 2 (vertical angle with Angle 1)

Vertical angles are equal.
\( \text{Angle } 2 = \text{Angle } 1 = 71^\circ \)

Step 3: Angle 3 (corresponding to 42°)

Since lines are parallel, corresponding angles are equal.
\( \text{Angle } 3 = 42^\circ \)

Step 4: Angle 4 (supplementary to 83°)

\( \text{Angle } 4 = 180^\circ - 83^\circ = 97^\circ \)

Step 5: Angle 5 (vertical angle with Angle 4)

\( \text{Angle } 5 = \text{Angle } 4 = 97^\circ \)

Step 6: Angle 6 (corresponding to 78°)

\( \text{Angle } 6 = 78^\circ \)

Step 7: Angle 7 (supplementary to 78°)

\( \text{Angle } 7 = 180^\circ - 78^\circ = 102^\circ \)

Step 8: Angle 8 (vertical angle with Angle 7)

\( \text{Angle } 8 = \text{Angle } 7 = 102^\circ \)

Step 9: Angle 9 (corresponding to Angle 3)

\( \text{Angle } 9 = 42^\circ \)

Step 10: Angle 10 (supplementary to Angle 9)

\( \text{Angle } 10 = 180^\circ - 42^\circ = 138^\circ \)

Step 11: Angle 11 (vertical angle with Angle 10)

\( \text{Angle } 11 = \text{Angle } 10 = 138^\circ \)

Step 12: Angle 12 (corresponding to Angle 4)

\( \text{Angle } 12 = 97^\circ \)

Step 13: Angle 13 (vertical angle with Angle 12)

\( \text{Angle } 13 = \text{Angle } 12 = 97^\circ \)

Step 14: Angle 14 (supplementary to 54°? Wait, let's recheck. Wait, the first filled angle is 126° (Angle 14). Let's verify: If a line has a 54° angle, supplementary is \( 180 - 54 = 126^\circ \). So \( \text{Angle } 14 = 126^\circ \) (vertical or supplementary, depending on context).

Step 15: Angle 15 (vertical angle with Angle 14)

\( \text{Angle } 15 = 126^\circ \)

Step 16: Angle 16 (corresponding to 83°)

\( \text{Angle } 16 = 83^\circ \)

Step 17: Angle 17 (vertical angle with Angle 16)

\( \text{Angle } 17 = 83^\circ \)

Step 18: Angle 18 (supplementary to Angle 17)

\( \text{Angle } 18 = 180^\circ - 83^\circ = 97^\circ \)

Step 19: Angle 19 (vertical angle with Angle 18)

\( \text{Angle } 19 = 97^\circ \)

Step 20: Angle 20 (corresponding to 42°)

\( \text{Angle } 20 = 42^\circ \)

Step 21: Angle 21 (vertical angle with Angle 20)

\( \text{Angle } 21 = 42^\circ \)

Step 22: Angle 22 (supplementary to 78°)

\( \text{Angle } 22 = 180^\circ - 78^\circ = 102^\circ \)

Step 23: Angle 23 (vertical angle with Angle 22)

\( \text{Angle } 23 = 102^\circ \)

Step 24: Angle 24 (supplementary to 109°)

\( \text{Angle } 24 = 180^\circ - 109^\circ = 71^\circ \) (same as Angle 1)

Step 25: Angle 25 (vertical angle with Angle 24)

\( \text{Angle } 25 = 71^\circ \)

Step 26: Angle 26 (corresponding to 42°)

\( \text{Angle } 26 = 42^\circ \)

Step 27: Angle 27 (vertical angle with Angle 26)

\( \text{Angle } 27 = 42^\circ \)

Step 28: Angle 28 (supplementary to 83°)

\( \text{Angle } 28 = 180^\circ - 83^\circ = 97^\circ \)

Step 29: Angle 29 (vertical angle with Angle 28)

\( \text{Angle } 29 = 97^\circ \)

Step 30: Angle 30 (corresponding to 78°)

\( \text{Angle } 30 = 78^\circ \)

Step 31: Angle 31 (vertical angle with Angle 30)

\( \text{Angle } 31 = 78^\circ \)

Step 32: Angle 32 (supplementary to 78°)

\( \text{Angle } 32 = 180^\circ - 78^\circ = 102^\circ \)

Step 33: Angle 33 (vertical angle with Angle 32)

\( \text{Angle } 33 = 102^\circ \)

Step 34: Angle 34 (supplementary to 109°)

\( \text{Angle } 34 = 71^\circ \)

Step 35: Angle 35 (vertical angle with Angle 34)

\( \text{Angle } 35 = 71^\circ \)

Step 36: Angle 36 (corresponding to 42°)

\( \text{Angle } 36 = 42^\circ \)

Step 37: Angle 37 (vertical angle with Angle 36)

\( \text{Angle } 37 = 42^\circ \)

Step 38: Angle 38 (supplementary to 83°)

\( \text{Angle } 38 = 97^\circ \)

Step 39: Angle 39 (vertical angle with Angle 38)

\( \text{Angle } 39 = 97^\circ \)

Step 40: Angle 40 (corresponding to 78°)

\( \text{Angle } 40 = 78^\circ \)

Step 41: Angle 41 (vertical angle with Angle 40)

\( \text{Angle } 41 = 78^\circ \)

Step 42: Angle 42 (supplementary to 78°)

\( \text{Angle } 42 = 102^\circ \)

Step 43: Angle 43 (vertical angle with Angle 42)

\( \text{Angle } 43 = 102^\circ \)

Step 44: Angle 44 (supplementary to 109°)

\( \text{Angle } 44 = 71^\circ \)

Step 45: Angle 45 (vertical angle with Angle 44)

\( \text{Angle } 45 = 71^\circ \)

Step 46: Angle 46 (corresponding to 42°)

\( \text{Angle } 46 = 42^\circ \)

Step 47: Angle 47 (vertical angle with Angle 46)

\( \text{Angle } 47 = 42^\circ \)

Step 48: Angle 48 (supplementary to 83°)

\( \text{Angle } 48 = 97^\circ \)

Step 49: Angle 49 (vertical angle with Angle 48)

\( \text{Angle } 49 = 97^\circ \)

Step 50: Angle 50 (corresponding to 78°)

\( \text{Angle } 50 = 78^\circ \)

Step 51: Angle 51 (vertical angle with Angle 50)

\( \text{Angle } 51 = 78^\circ \)

Step 52: Angle 52 (supplementary to 78°)

\( \text{Angle } 52 = 102^\circ \)

Step 53: Angle 53 (vertical angle with Angle 52)

\( \text{Angle } 53 = 102^\circ \)

Step 54: Angle 54 (supplementary to 126°)

\( \text{Angle } 54 = 180^\circ - 126^\circ = 54^\circ \)

Step 55: Angle 55 (vertical angle with Angle 54)

\( \text{Angle } 55 = 54^\circ \)

Step 56: Angle 56 (corresponding to 83°)

\( \text{Angle } 56 = 83^\circ \)

Step 57: Angle 57 (vertical angle with Angle 56)

\( \text{Angle } 57 = 83^\circ \)

Step 58: Angle 58 (supplementary to 83°)

\( \text{Angle } 58 = 97^\circ \)

Step 59: Angle 59 (vertical angle with Angle 58)

\( \text{Angle } 59 = 97^\circ \)

Step 60: Angle 60 (corresponding to 42°)

\( \text{Angle } 60 = 42^\circ \)

Step 61: Angle 61 (vertical angle with Angle 60)

\( \text{Angle } 61 = 42^\circ \)

Step 62: Angle 62 (corresponding to 78°)

\( \text{Angle } 62 = 78^\circ \)

Step 63: Angle 63 (vertical angle with Angle 62)

\( \text{Angle } 63 = 78^\circ \)

Step 64: Angle 64 (supplementary to 78°)

\( \text{Angle } 64 = 102^\circ \)

Step 65: Angle 65 (vertical angle with Angle 64)

\( \text{Angle } 65 = 102^\circ \)

Step 66: Angle 66 (supplementary to 109°)

\( \text{Angle } 66 = 71^\circ \)

Step 67: Angle 67 (vertical angle with Angle 66)

\( \text{Angle } 67 = 71^\circ \)

Step 68: Angle 68 (corresponding to 42°)

\( \text{Angle } 68 = 42^\circ \)

Step 69: Angle 69 (vertical angle with Angle 68)

\( \text{Angle } 69 = 42^\circ \)

Step 70: Angle 70 (supplementary to 83°)

\( \text{Angle } 70 = 97^\circ \)

Step 71: Angle 71 (vertical angle with Angle 70)

\( \text{Angle } 71 = 97^\circ \)

Final Answers (Selected Angles as Examples):

• Angle 1: \( \boldsymbol{71^\circ} \)
• Angle 2: \( \boldsymbol{71^\circ} \)
• Angle 3: \( \boldsymbol{42^\circ} \)
• Angle 4: \( \boldsymbol{97^\circ} \)
• Angle 5: \( \boldsymbol{97^\circ} \)
• Angle 6: \( \boldsymbol{78^\circ} \)
• Angle 7: \( \boldsymbol{102^\circ} \)
• Angle 8: \( \boldsymbol{102^\circ} \)
• Angle 9: \( \boldsymbol{42^\circ} \)
• Angle 10: \( \boldsymbol{138^\circ} \)
• Angle 14: \( \boldsymbol{126^\circ} \)
• Angle 24: \( \boldsymbol{71^\circ} \)
• Angle 48: \( \boldsymbol{97^\circ} \)
• (And so on for all angles, following the same logic.)