Question

Two angles lie along a straight line. If m∠A is five times the sum of m∠B plus 7.2°, what is m∠B?

Answer 1

Given:

m∠A = 5 × (m∠B + 7.2°)

To find:

The measure of m∠B

Solution:

m∠A = 5(m∠B + 7.2°)

Sum of adjacent angles in a straight line = 180°

m∠A + m∠B = 180°

5 × (m∠B + 7.2°) + m∠B = 180°

5 m∠B + 36° + m∠B = 180°

6 m∠B + 36° = 180°

Subtract 36° from both sides.

6 m∠B + 36° - 36° = 180° - 36°

6 m∠B = 144°

Divide by 6 on both sides, we get

m∠B = 24°

The measure of ∠B is 24°.

Answer 2

The angle of m∠B should be 24 degrees when the m∠A is five times the sum of m∠B plus 7.2°.

Calculation of the angle:

Since

m∠A = 5 × (m∠B + 7.2°)

So,

m∠A = 5(m∠B + 7.2°)

Also we know that

Sum of adjacent angles in a straight line = 180°

Now

m∠A + m∠B = 180°

5 × (m∠B + 7.2°) + m∠B = 180°

5 m∠B + 36° + m∠B = 180°

6 m∠B + 36° = 180°

6 m∠B = 144°

m∠B = 24°

Hence, The measure of ∠B is 24°.

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