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Two angles are complementary. The larger angle is 16 degrees larger than the smaller angle. Find the measure of both angles?

1 Answer
Mar 8, 2018

Answer:

#color(brown)(hat A = 53^@, hat B = 37^@#

Explanation:

Two angles are said to be complementary, if their sum equals #90^@#

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Let the two angles be #hat A, hatB#

Given #hat A + hat B = 90^@# Eqn (1)

Also given #hat A = hat B + 16#

Substituting value of #hat A# in terms of #hat B# in Eqn (1),

#(hat B + 16) + hat B= 90#

#2 hat B = 90 - 16 74#

#hat B = 74 / 2 = color (brown)(37^@#

Substituting value of #hat B# in Eqn (1),

#hat A = 90 - 37 = color(brown)(53^@#