Question

Use the elimination method when solving the translated system Two angles are complementary. (Complementary angles are angles whose sum is 90). Their dIfference is 52. Find the angles.The larger angle is?, and the smaller angle is ?

Answer 1

ANSWER

The larger angle is 71° and the smaller angle is 19°.

EXPLANATION

Let the first angle be x.

Let the second angle be y.

The two angles add up to 90 degrees. This implies that:

$x+y=90$

The difference between the two angles is 52. This implies that:

$x-y=52$

Now, we have a system of simultaneous equations:

$\begin{gathered} x+y=90 \\ x-y=52 \end{gathered}$

To solve by elimination, add the two equations to eliminate y:

$\begin{gathered} x+y+x-y=90+52 \\ x+x+y-y=142 \\ 2x=142 \\ x=\frac{142}{2} \\ x=71\degree \end{gathered}$

To find the value of y, substitute the value of x into the first equation:

$\begin{gathered} 71+y=90 \\ \Rightarrow y=90-71 \\ y=19\degree \end{gathered}$

Hence, the larger angle is 71° and the smaller angle is 19°.