Angle Relationships unit pack (Grades 7-8 · CCSS 7.G.B.5, 8.G.A.5): every worksheet and exit ticket for this unit, ready to print in one go. The answer keys print at the end, each on its own page, so you can leave them off. To make a PDF, click Print and choose "Save as PDF." Games: Bank Shot · Math Billiards · Laser Heist
Complementary and Supplementary Angles
Grade 7 · CCSS 7.G.B.5 · Pairs with the Bank Shot: Angle Golf game
Name
Date
Complementary angles add to 90° (they make a right angle, often marked with a small box).
Supplementary angles add to 180° (they make a straight line). To find the missing angle, subtract the one you know.
Key vocabulary
angle: the figure formed by two rays that share an endpoint
degree (°): the unit for measuring angles; a full turn is 360°
right angle: an angle of exactly 90°, often marked with a small square
straight angle: an angle of exactly 180°; its sides form a straight line
complementary angles: two angles whose measures add to 90° (35° and 55°)
supplementary angles: two angles whose measures add to 180° (110° and 70°)
Part A: Complementary angles
1.
? = °
2.
? = °
3. The complement of 80°
= °
4. The complement of 47°
= °
Part B: Supplementary angles
5.
? = °
6.
? = °
7. The supplement of 160°
= °
8. The supplement of 91°
= °
Part C: Vertical angles and missing-angle equations
9. Two lines cross. One angle is 64°. Find the angle across from it.
? = °
10. The two angles make a straight line. The missing angle is (x + 6)°. Find x. (Hole-In-One Hero)
x =
Part D: Equations and reasoning
11. An angle and its complement differ by 20°. Find both angles.
angles:
12. An angle is 4 times its supplement. Find both angles.
angles:
13. Can an angle of 110° have a complement? Explain.
14.Find the mistake. Chris said the supplement of 75° is 15°. What went wrong? What's the right answer?
Exit Ticket: Complementary and Supplementary Angles
Grade 7 · CCSS 7.G.B.5
Name
1. An angle is 47°. Find its complement and its supplement.
comp. ° supp. °
2. Two angles make a right angle. One is 50° and the other is (x − 4)°. Find x.
x =
3. Can an angle greater than 90° have a complement? A supplement? Explain.
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)
1.
? = °
2.
? = °
3.
? = °
4.
? = °
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?
3. A shot meets the cushion, making 134° with it on one side. What angle does it make on the other side? Name the relationship.
°
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°.
Key vocabulary
complementary angles: two angles whose measures add to 90°
supplementary angles: two angles whose measures add to 180°
vertical angles: the angles across from each other where two lines cross; they are equal
parallel lines: lines in the same plane that never meet
transversal: a line that crosses two or more other lines
corresponding angles: angles in the same position at each crossing; equal when the lines are parallel
alternate interior angles: angles between the parallel lines, on opposite sides of the transversal; equal
co-interior (same-side interior) angles: 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)
1.
? = °
2.
? = °
3.
? = °
4.
? = °
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: °
Part E: Laser puzzles (like the game: the laser turns by the whole marked angle to hit the panel)
12. Equal, or add to 180°? (circle) equal / add to 180°
x = °
13. Equal, or add to 180°? (circle) equal / add to 180°
x = °
14. The two lines are parallel. Equal, or add to 180°? (circle) equal / add to 180°
x = °
Part F: Any of the eight angles (like Floor 4 of the game: one angle is given, x can be any of the other seven)
The two lines are parallel. Find x. Then color-code: shade every angle equal to the given angle in one color (yellow) and every angle equal to x in another (blue). Every angle is one or the other.
3. Two complementary angles are x° and (x + 20)°. Find both angles.
angles:
Answer Key: Complementary and Supplementary Angles
For the teacher
90 − 35 = 55°
90 − 62 = 28°
10°
43°
180 − 128 = 52°
180 − 75 = 105°
20°
89°
Vertical angles are equal: 64°
180 − 70 = 110, so x + 6 = 110 → x = 104
x + (x + 20) = 90, 2x = 70 → 35° and 55°
x + 4x = 180, x = 36 → 36° and 144°
No. Complementary angles add to 90°, and 110° is already more than 90°.
Chris subtracted from 90° (the complement). Supplementary angles add to 180°: 105°
In the game, an answer that's off by 10° sends the ball 10° off course, so precision shows up right on the green. Straight shots in the game ask vertical-angle questions like #9, and Hole-In-One Hero writes some missing angles as equations like #10.
No complement (it's already more than 90°), but yes, a supplement, as long as it's less than 180°.
Quick read: 40 on #2 means the student found the angle but didn't undo the
Quick read: 40 on #2 means the student found the angle but didn't undo the − 4; 36 means they undid it the wrong way. Hole-In-One Hero mode practices exactly this.
minus; 4; 36 means they undid it the wrong way. Hole-In-One Hero mode practices exactly this.
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°
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.
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°
Add to 180° (a straight line): 180 − 128 = x = 52°
Equal (vertical angles): x − 5 = 63, so x = 68
Add to 180° (co-interior): 70 + (x + 6) = 180, x + 6 = 110, so x = 104
Add to 180° (same-side exterior angles: both outside the lines, on the same side): 180 − 72 = x = 108°. The four sharp angles are 72° (yellow) and the four wide ones are 108° (blue):
Add to 180° (two steps: slide 108° up to the top crossing as a corresponding angle, where it makes a straight line with x): 180 − 108 = x = 72°. The four wide angles are 108° (yellow) and the four sharp ones are 72° (blue):
Look for the right-angle box: if it's there, the pair adds to 90°. In the game, the laser fires at exactly the angle a student types, so a wrong answer visibly misses the panel and the correct line is shown beside it.