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Chapter 2: Q24. (page 53)

If 鈭�Aand 鈭�B are supplementary, find the value of x, m鈭�Aand m鈭�B.

m鈭�A=2x,m鈭�B=x-15

Short Answer

Expert verified

The value of x is 65.

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

Step by step solution

01

Step 1. Definition of supplementary angles.

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

02

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掳.

Therefore, the relation between the angles A and B is:m鈭�A+m鈭�B=180掳

03

Step 3. Find the value of x.

Find the value of x by using the relation m鈭�A+m鈭�B=180掳.

Therefore,

role="math" localid="1646034362006" m鈭�A+m鈭�B=180掳2x+x-15=1803x-15=1803x=180+153x=195x=1953x=65

Therefore, the value of x is 65.

04

Step 4. Find the measure of the angle A.

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

Therefore,

m鈭�A=2x=2脳65=130

Therefore, the measure of angle A is 130掳.

05

Step 5. Find the measure of the angle B.

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

Therefore,

m鈭�B=x-15=65-15=50

Therefore, the measure of angle B is 50掳.

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