Question

An angle is 9 more than half of its supplement. Find the measure of the smaller angle.

Answer 1

The smaller angle = 66°

let x be the angle then $\frac{1}{2}$ (180 - x) + 9 represents 9 more than half of it's supplement

equating the 2 expressions gives

x = $\frac{1}{2}$ (180 - x ) + 9 → (distribute and simplify right side )

x = 90 - $\frac{1}{2}$ x + 9 = 99 - $\frac{1}{2}$ x

add $\frac{ 1}{2}$ x to both sides

$\frac{3}{2}$ x = 99

multiply both sides by 2 and divide by 3 gives

x = 66

the supplement of 66° is 180° - 66° = 114°

Thus the smaller angle is 66°