Find the two complementary angles

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°

​Ask Algebra House