Question

Two angles are complementary. One angle measures 32 degrees more than the other angle. Find the measure of the LARGER angle

Answer 1

`\begin{array}{l}\text{We\ have\ } \alpha +\beta =90\ \text{and} \ \beta =\alpha +32\text{\ then}\\\\\alpha +\alpha +32=90\\\\\Longrightarrow 2\alpha =90-32\\\\\Longrightarrow \alpha =(58)/(2) =29\\\\\therefore \beta =29+32=61\\\\\therefore \boxed{\text{The\ larger\ angle\ is\ 61\ degrees}}\end{array}`