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question 5
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which statement about the angles in this diagram is false?
select one:
a. <c = 36°
b. <d = 36°
c. <a = 36°
d. <g = 36°

Explanation:

Step1: Identify supplementary angles

The angle of $144^{\circ}$ and $\angle e$ are supplementary (linear - pair). So, $\angle e=180^{\circ}-144^{\circ}=36^{\circ}$.

Step2: Use angle - relationships in parallel lines

Since the lines are parallel, $\angle e$ and $\angle a$ are corresponding angles, so $\angle a = \angle e=36^{\circ}$.
$\angle e$ and $\angle d$ are alternate - interior angles, so $\angle d=\angle e = 36^{\circ}$.
$\angle d$ and $\angle g$ are vertical angles, so $\angle g=\angle d = 36^{\circ}$.
$\angle c$ and the $144^{\circ}$ angle are corresponding angles, so $\angle c = 144^{\circ}$.

Answer:

A. $\angle c = 36^{\circ}$