Question

Two parallel lines are cut by a transversal as shown below.

Suppose m 7=148°. Find m1 and m 2 and m4

Answer 1

m<1 = 148

m<4 = 32

Explanation:

<1 and <7 are alternate exterior angles. By the Alternate Exterior Angle Theorem, <1 and <7 are congruent and therefore m<1 = m<7. So m<1 = 148 degrees.

<3 and <7 are corresponding angles. By the Corresponding Angles Postulate, <3 and <7 are congruent and therefore m<3 = m<7. So m<3 = 148 degrees. <3 and <4 form a linear pair, and by the Linear Pair Postulate, <3 and <4 are supplementary and therefore m<3 + m<4 = 180. So m<4 = 180 - m<3 = 180 - 148 = 32 degrees.