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 18 °. the larger angle measures \\(\square\\)°.

Explanation:

Step1: Define the smaller angle

Let the smaller angle be \( x = 18^\circ \).

Step2: Express the larger angle

The larger angle \( y \) is \( 18^\circ \) more than three times the smaller angle. So, \( y = 3x + 18^\circ \). Substitute \( x = 18^\circ \) into the formula: \( y = 3\times18 + 18 \).

Step3: Calculate the larger angle

First, calculate \( 3\times18 = 54 \). Then, \( 54 + 18 = 72 \). Alternatively, since the angles are complementary, \( x + y = 90^\circ \), so \( y = 90 - x = 90 - 18 = 72 \).

Answer:

The larger angle measures \( 72^\circ \).