Question

Angles X and Y are supplementary. The measure of angle X is 6 more than twice angle Y. Find the measure of angles X and Y.

Answer 1

• m∠X=122 degrees

,

• m∠Y=58 degrees

Step-by-step explanation:

Two angles are supplementary if they add up to 180 degrees.

If angles X and Y are supplementary, we have that:

`\begin{gathered} Equation\; 1\colon m\angle X+m\angle Y=180^0 \\ \implies m\angle X=180^0-m\angle Y \end{gathered}`

Also, the measure of angle X is 6 more than twice angle Y.

`Equation\; 2\colon m\angle X=2m\angle Y+6`

Substituting the measure of angle X from above, we have:

`\begin{gathered} 180^0-m\angle Y=2m\angle Y+6 \\ 2m\angle Y+m\angle Y=180^0-6 \\ 3m\angle Y=174^0 \\ m\angle Y=(174^0)/(3) \\ m\angle Y=58^0 \end{gathered}`

Next, we find the measure of angle X.

`\begin{gathered} m\angle X=2m\angle Y+6 \\ =2*58+6 \\ =122^0 \end{gathered}`