An angle measures 72° less than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

Let x be the measure of the angle and y be the measure of its supplementary angle.

Since the angle measures 72° less than its supplementary angle, we have the equation:
x = y - 72

And since the angles are supplementary, we also have:
x + y = 180

Substitute x = y - 72 into the second equation:
y - 72 + y = 180
2y - 72 = 180
2y = 252
y = 126

Now, substitute y = 126 back into x = y - 72:
x = 126 - 72
x = 54

Therefore, the angle measures 54° and its supplementary angle measures 126°.

Answer 2

The measure of an angle is 85.4°. What is the measure of its complementary angle?

Answer 3

The complementary angle to a given angle is the angle that adds up to 90° with the given angle.

To find the measure of the complementary angle to an angle measuring 85.4°, subtract 85.4° from 90°:
90° - 85.4° = 4.6°

So, the complementary angle to an angle measuring 85.4° is 4.6°.

Answer 4

The measure of an angle is fourteen times the measure of its complementary angle. What is the measure of each angle?

Answer 5

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

Given that the angle is fourteen times the measure of its complementary angle, we have the equation:
x = 14y

Since the angles are complementary, we also have:
x + y = 90

Substitute x = 14y into the second equation:
14y + y = 90
15y = 90
y = 6

Now, substitute y = 6 back into x = 14y:
x = 14(6)
x = 84

Therefore, the angle measures 84° and its complementary angle measures 6°.

Answer 6

An angle measures 78° more than the measure of its supplementary angle. What is the measure of each angle?

Answer 7

Let x be the measure of the angle and y be the measure of its supplementary angle.

Since the angle measures 78° more than its supplementary angle, we have the equation:
x = y + 78

And since the angles are supplementary, we also have:
x + y = 180

Substitute x = y + 78 into the second equation:
y + 78 + y = 180
2y + 78 = 180
2y = 102
y = 51

Now, substitute y = 51 back into x = y + 78:
x = 51 + 78
x = 129

Therefore, the angle measures 129° and its supplementary angle measures 51°.

Answer 8

The measure of an angle is five times the measure of its complementary angle. What is the measure of each angle?

Answer 9

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

Given that the angle is five times the measure of its complementary angle, we have the equation:
x = 5y

Since the angles are complementary, we also have:
x + y = 90

Substitute x = 5y into the second equation:
5y + y = 90
6y = 90
y = 15

Now, substitute y = 15 back into x = 5y:
x = 5(15)
x = 75

Therefore, the angle measures 75° and its complementary angle measures 15°.