Question

in the figure below, ( mangle 2 = 127^circ ). find ( mangle 1 ), ( mangle 3 ), and ( mangle 4 ).

Explanation:

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

Vertical angles are congruent, so $m\angle1 = m\angle2 = 127^\circ$.

Step2: Find $m\angle3$ (supplementary angles)

$\angle2$ and $\angle3$ are supplementary, so $m\angle3 = 180^\circ - m\angle2 = 180^\circ - 127^\circ = 53^\circ$.

Step3: Find $m\angle4$ (vertical angles)

Vertical angles are congruent, so $m\angle4 = m\angle2 = 127^\circ$.

Answer:

$m\angle 1 = 127^\circ$, $m\angle 3 = 53^\circ$, $m\angle 4 = 127^\circ$