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 15° more than four times the other angle. the smaller angle measures 15°. the larger angle measures □°

Explanation:

Step1: Define the smaller angle

Let the smaller angle be \( x = 15^\circ \).

Step2: Express the larger angle

The larger angle is \( 4x + 15^\circ \). Substitute \( x = 15^\circ \): \( 4(15^\circ) + 15^\circ = 60^\circ + 15^\circ = 75^\circ \)? Wait, no, wait. Wait, complementary angles sum to \( 90^\circ \). Wait, maybe I misread. Wait, let's re - do. Let the smaller angle be \( x \). Then the larger angle is \( 4x + 15 \). Since they are complementary, \( x+(4x + 15)=90 \). Solve for \( x \): \( 5x+15 = 90 \), \( 5x=75 \), \( x = 15 \). Then the larger angle is \( 4\times15 + 15=75 \)? Wait, no, \( 4x+15 \) when \( x = 15 \) is \( 4\times15+15 = 75 \), but \( 15 + 75=90 \), which is correct. Wait, but the problem says "the smaller angle measures \( 15^\circ \)", so the larger angle is \( 4\times15+15 = 75 \)? Wait, no, wait, \( 4x+15 \), \( x = 15 \), so \( 4\times15=60 \), \( 60 + 15=75 \). And \( 15+75 = 90 \), which is correct.

Answer:

\( 75 \)