Question

The figure shows a pair of parallel lines

intersected by another pair of parallel lines.
Are the measures of Z4 and 214 related in
the same way as the measures of 29 and
Z7? Show your work.

Answer 1

Explanation:

m∠4 + m∠16 = 180° [Consecutive exterior angles]

m∠16 = m∠14 [corresponding angles]

Therefore, m∠4 + m∠14 = 180°

m∠7 + m∠11 = 180° [Consecutive interior angles]

m∠11 = m∠9 [Corresponding angles]

Therefore, m∠7 + m∠9 = 180°

In both the cases sum of the given angles is 180°.

Therefore, measure of ∠4 and ∠14 are related in the same way as the measurement of ∠9 and ∠7.