Question

An angle measures 42.6° more than the measure of a complementary angle. What is the measure of each angle?

Answer 1

The two complementary angles measure 23.7° and 66.3°, where the smaller angle is 23.7° and the larger angle is 42.6° more than the smaller, resulting in a measure of 66.3°.

Step-by-step explanation:

To solve for the measures of two complementary angles where one angle is 42.6° more than the other, we start with the definition of complementary angles. Two angles are complementary if their measures add up to 90°. Let's assign the measure of the smaller angle as x degrees. Therefore, the measure of the larger angle is x + 42.6°. The equation based on the definition of complementary angles will be:

x + (x + 42.6°) = 90°

Simplifying the equation:

2x + 42.6° = 90°

2x = 90° - 42.6°

2x = 47.4°

x = 47.4° / 2

x = 23.7°

Thus, the measure of the smaller angle is 23.7°, and the measure of the larger angle is 23.7° + 42.6° = 66.3°.

Answer 2

x= one angle
90-x= complementary angle ( complementary angles adds up to 90 degrees)
x=90-x+42.6
x=-x+132.6(combine like terms)
x+x=-x+132.6+x(add x on both sides)
x=66.3(divide each side by 2)
90-66.3=2
one angle is 42.6 complentary angle is 88 degrees