Answer Keys: Angle Relationships

Student Concept Worksheet Answers

1

Equation: 42 + x = 90 | Missing angle: 48 degrees

Complementary angles sum to 90. 90 - 42 = 48 degrees.

2

Equation: 98 + x = 180 | Missing angle: 82 degrees

Supplementary angles sum to 180. 180 - 98 = 82 degrees.

3

Vertical: 75 degrees | Adjacent angles: 105 degrees and 105 degrees

Vertical angles are equal (75). Adjacent angles are supplementary: 180 - 75 = 105 degrees.

4

Angle 5: 65 degrees | Angle 6: 115 degrees | Sum: 180 degrees

Angle 5 is corresponding to angle 1 (equal). Angle 6 is supplementary to angle 5. Same-side interior angles are supplementary (add to 180).

Practice Worksheet Answers

Part A: Complementary and Supplementary Angles

#	Problem	Answer	Explanation
1	Complementary, one = 37	53 degrees	90 - 37 = 53
2	Supplementary, one = 112	68 degrees	180 - 112 = 68
3	Complementary, one = 63	27 degrees	90 - 63 = 27
4	Supplementary, one = 45	135 degrees	180 - 45 = 135

Part B: Vertical and Adjacent Angles

5

a = 122, b = 58, c = 122

Angle a (adjacent to 58) = 180 - 58 = 122. Angle b (vertical to 58) = 58. Angle c (vertical to a) = 122.

6

Vertical: 127 degrees | Adjacent: 53 degrees and 53 degrees

Vertical angles are equal: 127. Adjacent angles: 180 - 127 = 53.

Part C: Writing and Solving Equations

7

Equation: (2x + 5) + 3x = 90 | x = 17 | Angles: 39 and 51 degrees

5x + 5 = 90, 5x = 85, x = 17. First angle: 2(17) + 5 = 39. Second angle: 3(17) = 51. Check: 39 + 51 = 90.

8

Equation: (4x - 10) + (2x + 40) = 180 | x = 25 | Angles: 90 and 90 degrees

6x + 30 = 180, 6x = 150, x = 25. First angle: 4(25) - 10 = 90. Second angle: 2(25) + 40 = 90.

9

Equation: 5x + 15 = 8x - 30 | x = 15 | Angle: 90 degrees

Vertical angles are equal. 5x + 15 = 8x - 30, 45 = 3x, x = 15. Angle: 5(15) + 15 = 90.

Part D: Parallel Lines and Transversals

10

a) 72 | b) 108 | c) 72 | d) 72

a) Corresponding angles are equal. b) Supplementary to angle 1: 180 - 72 = 108. c) Vertical to angle 1: equal. d) Alternate interior angles are equal.

11

Relationship: Corresponding (equal) | Equation: 3x + 15 = 5x - 25 | x = 20

Angles 2 and 6 are corresponding angles. 3x + 15 = 5x - 25, 40 = 2x, x = 20.

12

x = 25 | Angle 3 = 80 degrees | Angle 5 = 100 degrees

Same-side interior angles are supplementary. (2x + 30) + 4x = 180, 6x + 30 = 180, x = 25. Angle 3: 2(25) + 30 = 80. Angle 5: 4(25) = 100.

Part E: Word Problems

13

65 degrees

The ramp, ground, and wall form a right triangle. The angle at the wall = 90 - 25 = 65 degrees (complementary).

14

Acute: 45 degrees | Obtuse: 135 degrees

Let acute = x, obtuse = 3x. x + 3x = 180, 4x = 180, x = 45. Obtuse = 3(45) = 135.

Challenge Problem #15:

x = 20, y = 110 degrees, z = 70 degrees

(3x + 10) and (5x - 30) are corresponding angles, so they're equal:

3x + 10 = 5x - 30

40 = 2x, x = 20

Angle (3x + 10) = 3(20) + 10 = 70 degrees

y is supplementary to 70: y = 180 - 70 = 110 degrees

z is vertical to (5x - 30) = 70 degrees

FAST Practice Quiz Answers

1

C) 107 degrees

Supplementary angles sum to 180. 180 - 73 = 107. A is the complement (wrong sum). B assumes equal (wrong). D adds incorrectly.

2

A) 45 degrees

Adjacent angles are supplementary (form a straight line). x = 180 - 135 = 45 degrees. C would be the vertical angle.

3

B) 54 degrees

Ratio 2:3 means 2x + 3x = 90, 5x = 90, x = 18. Larger angle = 3(18) = 54 degrees. The smaller angle is 36 degrees.

4

Select: Angle 3, Angle 5, and Angle 7

Angle 3 (vertical to 1) = 65 - vertical angles are equal
Angle 4 (adjacent to 1) = 115 - supplementary, not equal
Angle 5 (corresponding to 1) = 65 - corresponding angles are equal
Angle 6 is NOT alternate exterior to angle 1
Angle 7 (alternate interior to 3) = 65 - alternate interior angles are equal

5

B) 35

(2x + 15) + (3x - 10) = 180. 5x + 5 = 180. 5x = 175. x = 35.

6

B) 84 degrees

Same-side interior angles are supplementary. (4x + 20) + 6x = 180. 10x + 20 = 180. 10x = 160. x = 16. Angles: 4(16) + 20 = 84 and 6(16) = 96. Smaller is 84.

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