Chapter 5: Q2 (page 168)

Suppose that $∠ M$ 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 $90 °$ .

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, $G R ∥ M A$ and $G M ∥ R A$ .

The relation between $∠ G$ and $∠ M$ is shown below.

$∠ G + ∠ M = 180 °$

It is known that $∠ M = 90 °$

Thus,

$\begin{matrix} ∠ G + 90 ° = 180 ° \\ ∠ G = 180 ° - 90 ° \\ = 90 ° \end{matrix}$

Step 2. Determine the value of angle R

As GRAM is a parallelogram and opposite sides of a parallelogram are parallel, $G R ∥ M A$ and $G M ∥ R A$ .

The relation between $∠ G$ and $∠ R$ is shown below.

$∠ G + ∠ R = 180 °$

It is known that $∠ G = 90 °$

Thus,

$\begin{matrix} 90 ° + ∠ R = 180 ° \\ ∠ R = 180 ° - 90 ° \\ = 90 ° \end{matrix}$

Step 3. Determine the value of angle A

As GRAM is a parallelogram and opposite sides of a parallelogram are parallel, $G R ∥ M A$ and $G M ∥ R A$ .

The relation between $∠ R$ and $∠ A$ is shown below.

$∠ R + ∠ A = 180 °$

Now, it is known that $∠ R = 90 °$

Thus,

$\begin{matrix} 90 ° + ∠ A = 180 ° \\ ∠ A = 180 ° - 90 ° \\ = 90 ° \end{matrix}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Step 1. Determine the value of angle G

Step 2. Determine the value of angle R

Step 3. Determine the value of angle A

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

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

Short Answer

Step by step solution

Step 1. Determine the value of angle G

Step 2. Determine the value of angle R

Step 3. Determine the value of angle A

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

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