Question

recall that two angles are complementary if the sum of their measures is 90°. find the measures of two complementary angles if one angle is 18° more than three times the other angle. the smaller angle measures \\(\square\\)°.

Explanation:

Step1: Define variables

Let the smaller angle be \( x^\circ \). Then the larger angle is \( (3x + 18)^\circ \) since it is \( 18^\circ \) more than three times the smaller angle.

Step2: Use complementary angle property

Since the two angles are complementary, their sum is \( 90^\circ \). So we set up the equation:
\( x + (3x + 18) = 90 \)

Step3: Solve the equation

First, combine like terms:
\( 4x + 18 = 90 \)
Then, subtract 18 from both sides:
\( 4x = 90 - 18 \)
\( 4x = 72 \)
Finally, divide both sides by 4:
\( x = \frac{72}{4} = 18 \)

Answer:

The smaller angle measures \( \boxed{18}^\circ \).