Question

If m || n, m<1 = (5x + 15), and m2 = (8x - 21)', what is m<3?
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Answer 1

∠ 3 = 105°

Explanation:

∠ 1 and ∠ 2 are alternate angles and are congruent , then

8x - 21 = 5x + 15 ( subtract 5x from both sides )

3x - 21 = 15 ( add 21 to both sides )

3x = 36 ( divide both sides by 3 )

x = 12

Then

∠ 1 = 5x + 15 = 5(12) + 15 = 60 + 15 = 75°

∠ 3 and ∠ 1 are same- side interior angles and sum to 180° , then

∠ 3 + 75° = 180° ( subtract 75° from both sides )

∠ 3 = 105°