Chapter 2: Q25. (page 53)

If $∠ A$ and $∠ B$ are supplementary, find the value of x, $m ∠ A$ and $m ∠ B$ .
$m ∠ A = x + 16$ , $m ∠ B = 2 x - 16$

Short Answer

Expert verified

The value of $x$ is 60.

The measures of the angles $A$ and $B$ are $76 °$ and $104 °$ .

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,

$m ∠ A + m ∠ B = 180 ° x + 16 + 2 x - 16 = 180 3 x = 180 x = \frac{180}{3} x = 60$

Therefore, the value of x is 60.

Step 4. Find the measure of the angle A.

Substitute 60 for x into to find the measure of the angle A.

Therefore,

$m ∠ A = x + 16 = 60 + 16 = 76$

Therefore, the measure of angle A is 76°.

Step 5. Find the measure of angle B.

Substitute 60 for x into to find the measure of the angle B.

Therefore,

$m ∠ B = 2 x - 16 = 2 \times 60 - 16 = 120 - 16 = 104$

Therefore, the measure of angle B is 104°.

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If $∠ A$ and $∠ B$ are supplementary, find the value of x, $m ∠ A$ and $m ∠ B$ .
$m ∠ A = x + 16$ , $m ∠ B = 2 x - 16$

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 angle B.

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If ∠Aand ∠B are supplementary, find the value of x, m∠Aand m∠B.m∠A=x+16,m∠B=2x-16

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 angle B.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

If $∠ A$ and $∠ B$ are supplementary, find the value of x, $m ∠ A$ and $m ∠ B$ .
$m ∠ A = x + 16$ , $m ∠ B = 2 x - 16$