Question

An angle measures 53.2° more than the measure of its complementary angle. What is the measure of each angle?

Answer 1

The angle measures 71.6 degrees, and its complementary angle measures 18.4 degrees

Explanation:

Let x be the measure of the angle, and y be the measure of its complementary angle.

We know that the sum of the measures of complementary angles is 90 degrees:

x + y = 90

We are also given that the angle x is 53.2 degrees more than its complementary angle y:

x = y + 53.2

Now we can substitute the second equation into the first equation to solve for y:

y + 53.2 + y = 90

2y + 53.2 = 90

2y = 36.8

y = 18.4

So the measure of the complementary angle is 18.4 degrees.

We can now use the second equation to find the measure of the angle x:

x = y + 53.2 = 18.4 + 53.2 = 71.6

So the measure of the angle is 71.6 degrees.

Therefore, the measures of the angle and its complementary angle are 71.6 degrees and 18.4 degrees, respectively.