Question

an angle is 51 less than triple its complement . find the measure of each angle

Answer 1

Let's call x the angle.

Remember that its complement refers to the difference 90 - x, since complementary angles sum 90°.

Having said that, we express the following expression.

$x=3(90-x)-51$

Notice that we multiplied its complement by 3 to make it triple, then we subtracted 51 since the angle x is 51 less.

Let's solve for x now

$\begin{gathered} x=270-3x-51=219-3x \\ x+4x=219 \\ 5x=219 \\ x=\frac{219}{5}=43.8 \end{gathered}$

Therefore, one angle is 43.8°, let's find its complement.

$90-x=90-43.8=46.2$

Therefore, the second angle is 46.2°.