Question

Suppose that $\angle M$ is a right angle. What can you deduce about angles G, R, and A?

Short answer

The measure of each of the angles G, R, and A is $90°$.

Step-by-step solution

Step 1. Determine the value of angle G

As GRAM is a parallelogram and opposite sides of a parallelogram are parallel, $GR\parallel MA$and $GM\parallel RA$.

The relation between $\angle G$and $\angle M$is shown below.

$\angle G+\angle M=180°$

It is known that$\angle M=90°$

Thus,

$\begin{array}{c}\angle G+90°=180°\\ \angle G=180°-90°\\ =90°\end{array}$

Step 2. Determine the value of angle R

As GRAM is a parallelogram and opposite sides of a parallelogram are parallel, $GR\parallel MA$and $GM\parallel RA$.

The relation between $\angle G$and $\angle R$is shown below.

$\angle G+\angle R=180°$

It is known that$\angle G=90°$

Thus,

$\begin{array}{c}90°+\angle R=180°\\ \angle R=180°-90°\\ =90°\end{array}$

Step 3. Determine the value of angle A

As GRAM is a parallelogram and opposite sides of a parallelogram are parallel, $GR\parallel MA$and $GM\parallel RA$.

The relation between $\angle R$and $\angle A$is shown below.

$\angle R+\angle A=180°$

Now, it is known that $\angle R=90°$

Thus,

$\begin{array}{c}90°+\angle A=180°\\ \angle A=180°-90°\\ =90°\end{array}$