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 - angle relationship

Angle $g$ and angle $d$ are vertical angles. Vertical angles are equal. So, if $\angle g = 105^{\circ}$, then $\angle d=105^{\circ}$.

Step2: Identify supplementary - angle relationship

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

Step3: Identify vertical - angle relationship for $\angle c$

Angle $c$ and angle $b$ are vertical angles. Since vertical angles are equal, $\angle c=\angle b = 75^{\circ}$.

Step4: Identify corresponding - angle relationship for $\angle f$

Angle $f$ and angle $b$ are corresponding angles (because line $x$ is parallel to line $y$). Corresponding angles are equal when two parallel lines are cut by a transversal. So, $\angle f=\angle b = 75^{\circ}$.

Answer:

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