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Chapter 2: Q25. (page 53)

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

m鈭�A=x+16,m鈭�B=2x-16

Short Answer

Expert verified

The value of xis 60.

The measures of the angles A and B are 76掳 and 104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,

m鈭�A+m鈭�B=180掳x+16+2x-16=1803x=180x=1803x=60

Therefore, the value of x is 60.

04

Step 4. Find the measure of the angle A.

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

Therefore,

m鈭�A=x+16=60+16=76

Therefore, the measure of angle A is 76掳.

05

Step 5. Find the measure of angle B.

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

Therefore,

m鈭�B=2x-16=2脳60-16=120-16=104

Therefore, the measure of angle B is 104掳.

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