Question

Two angles are supplementary. One angle measures 52 degrees more than the other angle. Find the measure of the LARGER angle.

Answer 1

$\begin{array}{l}\text{We\ have\ } \alpha +\beta =180\ \text{and} \ \beta =\alpha +52\text{\ then}\\\\\alpha +\alpha +52=180\\\\\Longrightarrow 2\alpha =180-52\\\\\Longrightarrow \alpha =\frac{128}{2} =64\\\\\therefore \beta =64+52=116\\\\\therefore \boxed{\text{The\ larger\ angle\ is\ 116\ degrees}}\end{array}$