Question

The ratio of the measures of two complementary angles is 7:8. What is the measures of the smaller angles?

Answer 1

Consider that if x is the smaller angle and y is the grater angle, you can write:

`(x)/(y)=(7)/(8)`

the two angles are complementary, then, you can write:

`x+y=90`

In order to determine the values of x, proceed as follow:

Solve for y from the first equation:

`\begin{gathered} (x)/(y)=(7)/(8) \\ y=(8)/(7)x \end{gathered}`

Next, replace the previous expression into the second equation and solve for x:

`\begin{gathered} x+y=90 \\ x+(8)/(7)x=90 \\ (15)/(7)x=90 \\ x=(90)/(15)\cdot7=42 \end{gathered}`

Hence, the smaller angle is 42 degrees