Practice: Angle Relationships

5. Two lines intersect, forming 4 angles. One angle is 58 degrees.

Angle a =

Angle b =

Angle c =

6. Two lines intersect. One angle is 127 degrees. Find the other three angles.

Vertical angle:

Adjacent angles: and

7. Two angles are complementary. One angle is (2x + 5) degrees and the other is (3x) degrees.

Equation: ________________________________

x =

Angle measures: and

8. Two angles are supplementary. One angle is (4x - 10) degrees and the other is (2x + 40) degrees.

Equation: ________________________________

x =

Angle measures: and

9. Two vertical angles are (5x + 15) degrees and (8x - 30) degrees. Find x and the angle measures.

Equation: ________________________________

x =

Angle measure:

10. If angle 1 = 72 degrees, find the following:

a) Angle 5 (corresponding):

b) Angle 4 (supplementary to 1):

c) Angle 3 (vertical to 1):

d) Angle 6 (alternate interior to 3):

11. Using the same diagram, if angle 2 = (3x + 15) degrees and angle 6 = (5x - 25) degrees, find x.

(Hint: What is the relationship between angle 2 and angle 6?)

Relationship: ________________________________

Equation: ________________________________

x =

12. Angle 3 and angle 5 are same-side interior angles. If angle 3 = (2x + 30) degrees and angle 5 = (4x) degrees, find x and both angle measures.

x =

Angle 3 = Angle 5 =

13. A ramp makes an angle of 25 degrees with the ground. What is the measure of the angle between the ramp and the vertical wall? (Hint: The ground and wall form a 90-degree angle)

Answer: degrees

14. Two streets intersect. The acute angle formed is 3 times smaller than the obtuse angle. Find both angle measures. (Hint: Adjacent angles at an intersection are supplementary)

Acute angle: degrees

Obtuse angle: degrees