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°
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