Question

below, line x is parallel to line y. if the measure of angle g is 105°, find the angle measures for the following angles: measure of angle a = type your answer. measure of angle b = type your answer. measure of angle c = type your answer. measure of angle d = type your answer.

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. Angle $g$ and angle $a$ are vertical - angles. Since $\angle g = 105^{\circ}$, then $\angle a=105^{\circ}$.

Step2: Identify supplementary angles

Angle $a$ and angle $b$ are supplementary (linear pair). The sum of supplementary angles is $180^{\circ}$. So, $\angle b = 180^{\circ}-\angle a=180 - 105=75^{\circ}$.

Step3: Identify corresponding angles

Since line $x$ is parallel to line $y$, angle $b$ and angle $c$ are corresponding angles. Corresponding angles are equal when two lines are parallel. So, $\angle c=\angle b = 75^{\circ}$.

Step4: Identify vertical - angles again

Angle $c$ and angle $d$ are vertical - angles. Vertical angles are equal. So, $\angle d=\angle c = 75^{\circ}$.

Answer:

Measure of angle $a = 105^{\circ}$
Measure of angle $b = 75^{\circ}$
Measure of angle $c = 75^{\circ}$
Measure of angle $d = 75^{\circ}$