Question

If $\angle \mathbf{A}$and $\angle \mathbf{B}$ are supplementary, find the value of x, $\mathbf{m}\angle \mathbf{A}$and $\mathbf{m}\angle \mathbf{B}$.

$\mathbf{m}\angle \mathbf{A}\mathbf{=}\mathbf{2}\mathbf{x}$,$\mathbf{m}\angle \mathbf{B}\mathbf{=}\mathbf{x}-\mathbf{15}$

Short answer

The value of x is 65.

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

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:$m\angle A+m\angle B=180°$

Step 3. Find the value of x.

Find the value of x by using the relation $m\angle A+m\angle B=180°$.

Therefore,

role="math" localid="1646034362006" $$\begin{gathered} \begin{array}{c}m\angle A+m\angle B=180°\\ 2x+x-15=180\end{array} \\ \begin{array}{c}3x-15=180\\ 3x=180+15\end{array} \\ \begin{array}{c}3x=195\\ x=\frac{195}{3}\end{array} \\ x=65 \end{gathered}$$

Therefore, the value of x is 65.

Step 4. Find the measure of the angle A.

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

Therefore,

$$\begin{gathered} m\angle A=2x \\ =2\times 65 \\ =130 \end{gathered}$$

Therefore, the measure of angle A is 130°.

Step 5. Find the measure of the angle B.

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

Therefore,

$$\begin{gathered} m\angle B=x-15 \\ =65-15 \\ =50 \end{gathered}$$

Therefore, the measure of angle B is 50°.