A free printable worksheet that pairs with the Laser Heist: Angle Breaker game. The worksheet prints first, and the answer key prints on its own page after it, so you can leave it off. To make a PDF, click Print and choose "Save as PDF."

Angle Relationships

Grades 7–8 · CCSS 7.G.B.5, 8.G.A.5 · Pairs with the Laser Heist: Angle Breaker game

Name

Date

Complementary angles add to 90°. Supplementary angles add to 180°. Vertical angles (across from each other) are equal.
Parallel lines cut by a transversal: corresponding and alternate interior angles are equal; co-interior (same-side interior) angles add to 180°.

Part A: Complementary and supplementary angles (find the missing angle)

? = °

Part B: Vertical and adjacent angles

5. Two lines cross. Find x and y.

x = ° y = °

6. Two lines cross. Find x and y.

x = ° y = °

Part C: Parallel lines cut by a transversal

7. The two lines are parallel and ∠2 = 65°. Find every other angle.

∠1 ∠3 ∠4 ∠5
∠6 ∠7 ∠8

8. Use the same diagram. Name the relationship:

a) ∠2 and ∠6:
b) ∠3 and ∠6:
c) ∠4 and ∠6:
d) ∠1 and ∠4:

Part D: Write and solve an equation

9. Two angles are complementary. One is x° and the other is 2x°. Find both angles.

x = angles:

10. Two angles are supplementary: (3x + 10)° and (x + 30)°. Find x and both angles.

x = angles:

11. Find the mistake. Dana said the complement of 35° is 145°. What did Dana do wrong? What's the correct answer?

Correct: °

Answer Key: Angle Relationships

For the teacher

90 − 34 = 56°
90 − 72 = 18°
180 − 118 = 62°
180 − 27 = 153°
x is vertical to 40° → x = 40°; y is adjacent (supplementary) → y = 140°
x = 115°; y = 65°
∠1 = 115°, ∠3 = 65°, ∠4 = 115°, ∠5 = 115°, ∠6 = 65°, ∠7 = 65°, ∠8 = 115°
a) corresponding (equal) b) alternate interior (equal) c) co-interior / same-side interior (add to 180°) d) vertical (equal)
x + 2x = 90, 3x = 90 → x = 30; angles 30° and 60°
4x + 40 = 180, 4x = 140 → x = 35; angles 115° and 65°
Dana subtracted from 180° (that's the supplement). Complementary angles add to 90°: 55°

Look for the right-angle box: if it's there, the pair adds to 90°. In the game, the camera cone in each maze is drawn from the angle the student solves, so a wrong answer changes where it's safe to walk.