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If Aand B are supplementary, find the value of x, mAand mB.

mA=2x,mB=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

01

Step 1. Definition of supplementary angles.

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

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°.

Therefore, the relation between the angles A and B is:mA+mB=180°

03

Step 3. Find the value of x.

Find the value of x by using the relation mA+mB=180°.

Therefore,

role="math" localid="1646034362006" mA+mB=180°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 mA=2x to find the measure of the angle A.

Therefore,

mA=2x=2×65=130

Therefore, the measure of angle A is 130°.

05

Step 5. Find the measure of the angle B.

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

Therefore,

mB=x-15=65-15=50

Therefore, the measure of angle B is 50°.

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