Angle relationships worksheet

Grade 7 math, Common Core 7.G.B.5. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Angle relationships

Grade 7 math, Common Core 7.G.B.5

Find each missing angle or the value of x.

1.
Two angles are complementary. One measures 78°. What does the other measure?
2.
Two angles are complementary. One measures 28°. What does the other measure?
3.
Two complementary angles measure x° and (2x + 18)°. Find x and both angles.
4.
Two angles are supplementary. One measures 84°. What does the other measure?
5.
Two lines cross. One angle measures 140°. What are the measures of its vertical angle and of the angle next to it?
6.
Two angles are complementary. One measures 14°. What does the other measure?
7.
Two lines cross. One angle measures 87°. What are the measures of its vertical angle and of the angle next to it?
8.
Two angles are supplementary. One measures 145°. What does the other measure?
9.
Two lines cross. One angle measures 90°. What are the measures of its vertical angle and of the angle next to it?
10.
Two supplementary angles measure (x + 6)° and (x − 4)°. Find x.

Answer key: Angle relationships

Grade 7 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. 12°
90 − 78 = 12
2. 62°
90 − 28 = 62
3. x = 24; the angles are 24° and 66°
x + 2x + 18 = 903x + 18 = 90x = 24
4. 96°
180 − 84 = 96
5. Vertical: 140°; next to it: 40°
Vertical angles are equalAngles next to each other on a line add to 180°
6. 76°
90 − 14 = 76
7. Vertical: 87°; next to it: 93°
Vertical angles are equalAngles next to each other on a line add to 180°
8. 35°
180 − 145 = 35
9. Vertical: 90°; next to it: 90°
Vertical angles are equalAngles next to each other on a line add to 180°
10. x = 89
x + 6 + x − 4 = 1802x + 2 = 180x = 89

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About angle relationships

Complementary angles add up to 90° and supplementary angles add up to 180°. Vertical angles are the opposite angles formed by two crossing lines, and they are always equal. Adjacent angles share a side. Write an equation from the relationship, then solve it.

Worked example 1

Two angles are supplementary. One measures 110°. What does the other measure?

Step 1.180 − 110 = 70

Answer: 70°

Worked example 2

Two lines cross. One angle measures 148°. What are the measures of its vertical angle and of the angle next to it?

Step 1.Vertical angles are equal
Step 2.Angles next to each other on a line add to 180°

Answer: Vertical: 148°; next to it: 32°

Worked example 3

Two complementary angles measure x° and (3x + 18)°. Find x and both angles.

Step 1.x + 3x + 18 = 90
Step 2.4x + 18 = 90
Step 3.x = 18

Answer: x = 18; the angles are 18° and 72°

Watch out for

Complementary is 90° (think C for corner), supplementary is 180° (S for straight).
Vertical angles are across from each other, not next to each other.
When angles are given as expressions, set up an equation and solve for x before finding the angles.

Practice angle relationships online

On StudyWiz, your kid can practice angle relationships with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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