27 in2
B.
31 in2
C.
45 in2
D.
47 in2
To find the measure of each angle, assume the measure of one angle is x degrees. The other angle measures 56° less than the measure of its complementary angle. Solve the equation to find the measures of the angles.
To find the measure of each angle, let's assume the measure of one angle is x degrees.
According to the problem, the other angle measures 56° less than the measure of its complementary angle, which means it is 90 - x - 56 = 34 - x degrees.
Since two angles are complementary, their sum should be equal to 90 degrees.
Therefore, x + (34 - x) = 90.
Solving the equation, we get x = 28 degrees and 34 - x = 34 - 28 = 6 degrees.
So, the measure of each angle is 28 degrees and 6 degrees, respectively.
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