Question

Find the measure of an angle whose supplement is thirteen times its complement. Hint. The supplement and complement of an angle are (180-0)⁰ and (90-0)⁰ respectively.

Answer 1

We have an angle X.

We know that the supplement, which has a value of (180-X) is 13 times its complement, which has a value (90-X).

We can write this as:

$\begin{gathered} (180-X)=13\cdot(90-X) \\ 180-X=1170-13X \\ 13X-X=1170-180 \\ 12X=990 \\ X=\frac{990}{12} \\ X=82.5 \end{gathered}$

The measure of this angle is 82.5 degrees.