Question

The measures of two complementary angles are described by the expressions (14x+5)° and (19x−14)°. Find the measures of the angles.

Answer 1

Complementary angles are those angles that together add up to 90°. Therefore:

`(14x+5)+(19x-14)=90`

And solve for x:

`\begin{gathered} 14x+5+19x-14=90 \\ Add\text{ / subtract like terms} \\ 33x-9=90 \end{gathered}`

Add 9 on both sides:

`\begin{gathered} 33x-9+9=90+9 \\ 33x=99 \\ \text{Divide by 33} \\ (33x)/(33)=(99)/(33) \\ x=3 \end{gathered}`

Next, we find the measures of the angles.

Angle 1:

`14x+5=14(3)+5=42+5=47`

Angle 2:

`19x-14=19(3)-14=57-14=43`

Answer:

Angle 1 = 47°

Angle 2 = 43°