Question

if m and n are parallel and angle 1 is 135°, what is the measure of angle 8? (1 point)

Explanation:

Step1: Find the measure of angle 3

Since angle 1 and angle 3 are vertical angles, they are equal. So, angle 3 = 135°.

Step2: Use the property of parallel lines and same - side interior angles

Since M and N are parallel, angle 3 and angle 5 are same - side interior angles. But we can also use the property of corresponding angles. Angle 1 and angle 5 are corresponding angles (if we consider the transversal). But another way: angle 3 and angle 7 are vertical angles (angle 7 = 135°). Angle 7 and angle 8 are supplementary (they form a linear pair).
Let \(x\) be the measure of angle 8. Then \(x+135^{\circ}=180^{\circ}\)

$$x = 180^{\circ}-135^{\circ}$$

Answer:

\(45\)