Question

question 9
give line x is parallel to line y and m∠angle2 = 23°. what is m∠m angle7?
157
60
(hint the angle that does not have the numbers inside.)
142
90

Explanation:

Step1: Identify vertical - angle relationship

$\angle2$ and $\angle4$ are vertical angles, so $m\angle4 = m\angle2=23^{\circ}$

Step2: Identify corresponding - angle relationship

Since line $x$ is parallel to line $y$, $\angle4$ and $\angle8$ are corresponding angles. So $m\angle8 = m\angle4 = 23^{\circ}$

Step3: Use linear - pair relationship

$\angle7$ and $\angle8$ form a linear pair. Since the sum of angles in a linear pair is $180^{\circ}$, we have $m\angle7=180 - m\angle8$
Substitute $m\angle8 = 23^{\circ}$ into the formula: $m\angle7=180 - 23=157^{\circ}$

Answer:

$157$