The measure of the first angle is 17°.
The measure of the second angle is 73°.
Solving for the Complementary Angles
Let x be the measure of the first angle. We know that its complementary angle measures 56° more than x. Therefore, the measure of the complementary angle is (x + 56)°.
Since complementary angles add up to 90°, we can set up the following equation:
x + (x + 56) = 90°
Combining like terms, we get:
2x + 56 = 90°
Subtracting 56 from both sides, we have:
2x = 34°
Dividing both sides by 2, we find:
x = 17°
Therefore, the measure of the first angle is 17°.
Now we can find the measure of the complementary angle:
x + 56 = 17° + 56° = 73°
Therefore, the measure of the second angle is 73°.