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Chapter 5: Q2 (page 168)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Determine the value of angle G

As GRAM is a parallelogram and opposite sides of a parallelogram are parallel, GR鈭�MAand GM鈭�RA.

The relation between 鈭�Gand 鈭�Mis shown below.

鈭�G+鈭�M=180掳

It is known that鈭�M=90掳

Thus,

鈭�G+90掳=180掳鈭�G=180掳鈭�90掳=90掳

02

Step 2. Determine the value of angle R

As GRAM is a parallelogram and opposite sides of a parallelogram are parallel, GR鈭�MAand GM鈭�RA.

The relation between 鈭�Gand 鈭�Ris shown below.

鈭�G+鈭�R=180掳

It is known that鈭�G=90掳

Thus,

90掳+鈭�R=180掳鈭�R=180掳鈭�90掳=90掳

03

Step 3. Determine the value of angle A

As GRAM is a parallelogram and opposite sides of a parallelogram are parallel, GR鈭�MAand GM鈭�RA.

The relation between 鈭�Rand 鈭�Ais shown below.

鈭�R+鈭�A=180掳

Now, it is known that 鈭�R=90掳

Thus,

90掳+鈭�A=180掳鈭�A=180掳鈭�90掳=90掳

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