Question

question 7 1 pts
given line x is parallel to line y and ( mangle2 = 23^{circ}).
what is ( mangle7)?

Explanation:

Step1: Find \(m\angle4\)

Since \(\angle2\) and \(\angle4\) are supplementary (\(\angle2+\angle4 = 180^{\circ}\)), and \(m\angle2=23^{\circ}\), then \(m\angle4=180 - 23=157^{\circ}\).

Step2: Use parallel - line property

Because line \(x\parallel\) line \(y\), \(\angle4\) and \(\angle6\) are alternate interior angles, so \(m\angle6 = m\angle4=157^{\circ}\).

Step3: Find \(m\angle7\)

Since \(\angle6\) and \(\angle7\) are supplementary (\(\angle6+\angle7 = 180^{\circ}\)), then \(m\angle7=180 - 157 = 23^{\circ}\).

Answer:

\(23^{\circ}\)