Question

hw 1.3.4 angles formed by intersecting lines
the ratio of the measure of an angle to its complement is 3:2.
what is the measure of the smaller angle?

Explanation:

Step1: Let the angle be $x$.

Its complement is $90 - x$.

Step2: Set up the ratio equation.

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

Step3: Cross - multiply.

$2x = 3(90 - x)$

Step4: Expand the right side.

$2x=270 - 3x$

Step5: Add $3x$ to both sides.

$2x + 3x=270$, so $5x = 270$

Step6: Solve for $x$.

$x=\frac{270}{5}=54$ degrees, and its complement is $90 - 54 = 36$ degrees.

Answer:

$36$ degrees