A free printable worksheet that pairs with the Math Billiards 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: Pool Shots

Grade 8 · CCSS 7.G.B.5, 8.G.A.5 · Pairs with the Math Billiards 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, alternate interior and alternate exterior angles are equal; same-side interior angles add to 180°.

Key vocabulary

complementary angles: two angles whose measures add to 90°
supplementary angles: two angles whose measures add to 180°; side by side on a line they form a linear pair
vertical angles: the angles across from each other where two lines cross; they are equal
transversal: a line that crosses two or more other lines
alternate interior angles: between the parallel lines, on opposite sides of the transversal; equal
same-side interior angles: between the parallel lines, on the same side of the transversal; they add to 180°

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

? = °

Part B: Vertical 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 = 64°. 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 ∠8:

Part D: Pool shots (like the game: the angle you find decides where the ball goes)

9. The cue ball rolls to the cushion. The dashed line is perpendicular to the cushion. Find x.

x = °

10. The path meets the cushion (a straight line). Find x.

x = °

11. A guide line crosses the shot's line at the cue ball. The dashed part runs back along the cue. Find x.

x = °

12. The guide line through the cue ball is parallel to the cushion. Find x and y.

x = ° y = °

Part E: Write and solve an equation

13. A right angle at the cue ball is split by the shot into x° and (2x + 15)°. Find both angles.

x = angles:

14. Find the mistake. A right angle at the cue ball is split into 62° and x. Jamal typed x = 118, and the ball went far off. What did he do wrong? What's x?

x = °

Answer Key: Angle Relationships: Pool Shots

For the teacher

90 − 55 = 35°
90 − 17 = 73°
180 − 145 = 35°
180 − 38 = 142°
x is vertical to 47° → x = 47°; y is adjacent (supplementary) → y = 133°
x = 128°; y = 52°
∠1 = 116°, ∠3 = 64°, ∠4 = 116°, ∠5 = 116°, ∠6 = 64°, ∠7 = 64°, ∠8 = 116°
a) corresponding (equal) b) alternate interior (equal) c) same-side interior (add to 180°) d) alternate exterior (equal)
The cushion and the perpendicular make a right angle: x + 32 = 90, x = 58°
A straight line: x + 121 = 180, x = 59°
Vertical angles are equal: x = 47°
Alternate interior: x = 64°. y and x are same-side interior angles: 180 − 64, y = 116°
x + 2x + 15 = 90, 3x = 75 → x = 25; angles 25° and 65°
Jamal subtracted from 180°, but the box means the parts add to 90°: x = 28°. (In the game, 118° really points the ball 90° away from the shot he aimed.)

In the game, a wrong answer plays the shot that angle really makes, then shows both paths. Problem 14 is a good one to act out: draw Jamal's 118° from the same guide line and see where it points.