Question

9. The measure of angle A is 60 degrees larger than twice theof the supplemental angle B. What is the measurement ofmeasurementangle A?40°140°180°60°

Answer 1

Two angles are called supplementary when their measures add up to 180 degrees.

If angles A and B are supplementary, it means that:

$A+B=180$

If the measure of angle A is 60 degrees larger than twice the of the supplemental angle B, it can be had that:

$A=2B+60$

Substitute the equation for A into the first equation:

$2B+60+B=180$

Solving for B:

$\begin{gathered} 3B+60=180 \\ 3B=180-60=120 \\ \therefore \\ B=\frac{120}{3} \\ B=40\degree \end{gathered}$

The measure of angle A can be gotten by substituting the value of B into the equation for A:

$\begin{gathered} A=2(40)+60 \\ A=80+60 \\ A=140\degree \end{gathered}$

The measure of A is 140°.