Question

Two angles are complementary. The larger of the two is 30° more than twice the smaller. Find the 2 angles

Answer 1

Let's call the measure of the larger angle as x, and the measure of the smaller angle as y.

When two angles are complementary, their sum is equal to 90º, therefore

`x+y=90`

The larger of the two is 30° more than twice the smaller, writing this as an equation, we have

`x=2y+30`

If we substitute this expression for x in the first equation, we have

`\begin{gathered} (x)+y=90 \\ (2y+30)+y=90 \\ 2y+30+y=90 \\ 3y+30=90 \\ 3y=90-30 \\ 3y=60 \\ y=(60)/(3) \\ y=20 \end{gathered}`

Using this y-value on the first expression, we have

`\begin{gathered} x+(20)=90 \\ x+20=90 \\ x=90-20 \\ x=70 \end{gathered}`

Then, the larger angle is 70º and the smaller angle is 20º.