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QuestionAn angle's supplement is three times the angle. Find the angle and its supplement. Let the angle be xx. Then, the supplement is 180−x=3x180 - x = 3x.

Studdy Solution

STEP 1

Assumptions1. The measure of the supplement of an angle is three times the measure of the angle. . The sum of an angle and its supplement is180 degrees.

STEP 2

Let's denote the measure of the angle as x. Therefore, the measure of the supplement of the angle isx.

STEP 3

According to the definition of supplementary angles, the sum of an angle and its supplement is180 degrees. Therefore, we can write the equationx+3x=180x +3x =180

STEP 4

Combine like terms on the left side of the equation.
4x=1804x =180

STEP 5

To solve for x, divide both sides of the equation by4.
x=1804x = \frac{180}{4}

STEP 6

Calculate the value of x.
x=1804=45x = \frac{180}{4} =45So, the measure of the angle is45 degrees.

STEP 7

Now, we can find the measure of the supplement of the angle by multiplying the measure of the angle by3.
Supplement=3xSupplement =3x

STEP 8

Plug in the value of x to calculate the measure of the supplement.
Supplement=3times45Supplement =3 \\times45

STEP 9

Calculate the measure of the supplement.
Supplement=3times45=135Supplement =3 \\times45 =135So, the measure of the supplement of the angle is135 degrees.
The measures of the angle and its supplement are45 degrees and135 degrees, respectively.

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