Question

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

$\mathbf{m}\angle \mathbf{A}\mathbf{=}\mathbf{x}\mathbf{+}\mathbf{16}$,$\mathbf{m}\angle \mathbf{B}\mathbf{=}\mathbf{2}\mathbf{x}\mathbf{-}\mathbf{16}$

Short answer

The value of $x$is 60.

The measures of the angles $A$ and $B$ are $76°$ and $104°$.

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,

$$\begin{gathered} m\angle A+m\angle B=180° \\ x+16+2x-16=180 \\ 3x=180 \\ x=\frac{180}{3} \\ x=60 \end{gathered}$$

Therefore, the value of x is 60.

Step 4. Find the measure of the angle A.

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

Therefore,

$$\begin{gathered} m\angle A=x+16 \\ =60+16 \\ =76 \end{gathered}$$

Therefore, the measure of angle A is 76°.

Step 5. Find the measure of angle B.

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

Therefore,

$$\begin{gathered} m\angle B=2x-16 \\ =2\times 60-16 \\ =120-16 \\ =104 \end{gathered}$$

Therefore, the measure of angle B is 104°.