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Two parallel lines are cut by a transversal as shown below.
Suppose m 7=148°. Find m1 and m 2 and m4

Two parallel lines are cut by a transversal as shown below Suppose m 7148 Find m1 and m 2 and m4 class=

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Answer:

m<1 = 148

m<4 = 32

Step-by-step 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.

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