Two angles are complementary if the sum of their measures is 90°. Find two complementary angles such that the smaller angle is 118° less than 3 times the larger angle.

**Complementary angles add up to 90°.**

x = larger angle

3x - 118 = smaller angle {smaller angle is 118° less than 3 times larger angle}

x + 3x - 118 = 90 {added the two angles and set equal to 90°}

4x - 118 = 90 {combined like terms}

4x = 208 {added 118 to each side}

x = 52 {divided each side by 4}

3x - 118 = 38 {substituted 52, in for x, into 3x - 118}

**smaller angle is 38°**

larger angle is 52°

larger angle is 52°

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