Question

the ratio of the measure of an angle to the measure of its complement is 2:3. what are the two angle measures?
a. 30° and 45°
b. 30° and 60°
c. 36° and 54°
d. 72° and 108°

Explanation:

Step1: Let the angle be $x$.

Its complement is $90 - x$.

Step2: Set up the ratio equation.

$\frac{x}{90 - x}=\frac{2}{3}$

Step3: Cross - multiply.

$3x = 2(90 - x)$

Step4: Expand the right side.

$3x=180 - 2x$

Step5: Add $2x$ to both sides.

$3x + 2x=180$, so $5x = 180$

Step6: Solve for $x$.

$x=\frac{180}{5}=36^{\circ}$

Step7: Find the complement.

The complement is $90 - 36=54^{\circ}$

Answer:

C. $36^{\circ}$ and $54^{\circ}$