Complementary Angles

Two angles are complementary. The sum of the measurement of the first angle and half the second angle is 84. Find the measures of the angles.  What is the measure of the smaller angle?  What is the measure of the other angle? 

x = one angle
90 - x = other angle   {the two angles are complementary....add up to 90} 

x + 1/2(90 - x) = 84   {sum of 1st and half 2nd is 84}
x + 45 - 1/2x = 84   {used distributive property}
1/2x + 45 = 84   {combined like terms}
1/2x = 39   {subtracted 45 from both sides}
x = 78   {divided both sides by 1/2....multiplied by 2}
90 - x = 12   {substituted 78, in for x, into 90 - x} 

smaller angle is 12 and other angle is 78

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