Chapter 2: Q24. (page 53)

If $∠ A$ and $∠ B$ are supplementary, find the value of x, $m ∠ A$ and $m ∠ B$ .
$m ∠ A = 2 x$ , $m ∠ B = x - 15$

Short Answer

Expert verified

The value of x is 65.

The measures of the angles A and B are 130° and 50°.

Step by step solution

Step 1. Definition of supplementary angles.

The supplementary angles are the angles whose sum is 180°.

Step 2. Write the relation between the angles A and B.

As the angles A andB are supplementary, therefore, the sum of the angles A andB is 180°.

Therefore, the relation between the angles A and B is: $m ∠ A + m ∠ B = 180 °$

Step 3. Find the value of x.

Find the value of x by using the relation $m ∠ A + m ∠ B = 180 °$ .

Therefore,

role="math" localid="1646034362006" $\begin{matrix} m ∠ A + m ∠ B = 180 ° \\ 2 x + x - 15 = 180 \end{matrix} \begin{matrix} 3 x - 15 = 180 \\ 3 x = 180 + 15 \end{matrix} \begin{matrix} 3 x = 195 \\ x = \frac{195}{3} \end{matrix} x = 65$

Therefore, the value of x is 65.

Step 4. Find the measure of the angle A.

Substitute 65 for x into $m ∠ A = 2 x$ to find the measure of the angle A.

Therefore,

$m ∠ A = 2 x = 2 \times 65 = 130$

Therefore, the measure of angle A is 130°.

Step 5. Find the measure of the angle B.

Substitute 65 for x into $m ∠ B = x - 15$ to find the measure of the angle B.

Therefore,

$m ∠ B = x - 15 = 65 - 15 = 50$

Therefore, the measure of angle B is 50°.

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.

If $∠ A$ and $∠ B$ are supplementary, find the value of x, $m ∠ A$ and $m ∠ B$ .
$m ∠ A = 2 x$ , $m ∠ B = x - 15$

Short Answer

Step by step solution

Step 1. Definition of supplementary angles.

Step 2. Write the relation between the angles A and B.

Step 3. Find the value of x.

Step 4. Find the measure of the angle A.

Step 5. Find the measure of the angle B.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Statistics

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

If ∠Aand ∠B are supplementary, find the value of x, m∠Aand m∠B.m∠A=2x,m∠B=x-15

Short Answer

Step by step solution

Step 1. Definition of supplementary angles.

Step 2. Write the relation between the angles A and B.

Step 3. Find the value of x.

Step 4. Find the measure of the angle A.

Step 5. Find the measure of the angle B.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Statistics

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

If $∠ A$ and $∠ B$ are supplementary, find the value of x, $m ∠ A$ and $m ∠ B$ .
$m ∠ A = 2 x$ , $m ∠ B = x - 15$