High School

Find the measures of complementary, supplementary, vertical, and adjacent angles.

The measure of an angle is nine times the measure of its supplementary angle. What is the measure of each angle?

Answer :

Answer:

The measure of the angle is 150°, the measure of its supplementary is 30°

Step-by-step explanation:

The given parameters are;

The measure of the given angle = 5 × The measure of its supplementary angle

Let "x" represent the given angle, and let "y" represent its supplementary angle, we have;

x = 5 × y...(1)

x + y = 180°...(2)

By substituting the value of x = 5 × y, from the first equation into the second equation, we have;

x + y = 180°

x + y = 5 × y + y = 5·y + y = 6·y = 180°

y = 180°/6 = 30°

y = 30°

x = 5 × y = 5 × 30° = 150°

x = 150°

The measure of the angle = x = 150°, the measure of its supplementary = y = 30°.

The measure of the angle is 162 degrees and the measure of its supplementary angle is 18 degrees.

Let x be the measure of the angle and y be the measure of its supplementary angle. We know that the sum of the measures of supplementary angles is 180 degrees. So, we can write the following equation:

x + y = 180

We also know that the measure of the angle is nine times the measure of its supplementary angle. So, we can write the following equation:

x = 9y

Now we have two independent equations, and we can solve for our two unknowns. One way to solve for x is to substitute the second equation into the first equation. This gives us:

(9y) + y = 180

Combining like terms, we get:

10y = 180

Dividing both sides by 10, we get:

y = 18

Now that we know the measure of the supplementary angle, we can substitute it into the second equation to solve for the measure of the angle. This gives us:

x = 9(18)

x = 162

Therefore, the measure of the angle is 162 degrees and the measure of its supplementary angle is 18 degrees.

For such more question on supplementary:

https://brainly.com/question/12919120

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