Question

two parallel lines are cut by a transversal as shown below. suppose ( mangle 4 = 36^circ ). find ( mangle 5 ) and ( mangle 7 ).

Explanation:

Step1: Find $m\angle1$ (vertical angle)

$\angle1$ and $\angle4$ are vertical angles, so $m\angle1 = m\angle4 = 36^\circ$

Step2: Find $m\angle5$ (corresponding angles)

$\angle1$ and $\angle5$ are corresponding angles (parallel lines cut by transversal), so $m\angle5 = m\angle1 = 36^\circ$

Step3: Find $m\angle7$ (supplementary to $\angle5$)

$\angle5$ and $\angle7$ are supplementary (linear pair), so $m\angle7 = 180^\circ - m\angle5 = 180^\circ - 36^\circ = 144^\circ$

Answer:

$m\angle5 = 36^\circ$
$m\angle7 = 144^\circ$