What is the measure of the larger of two supplementary angles if the difference between the measures of the angles is 80?

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Supplementary angles are two angles whose measures add up to 180 ° .

The two angles of a linear pair , like ∠ 1     and     ∠ 2 in the figure below, are always supplementary.

But, two angles need not be adjacent to be supplementary. In the next figure, ∠ 3     and     ∠ 4 are supplementary, because their measures add to 180 ° .

Example 1:

Two angles are supplementary. If the measure of the angle is twice the measure of the other, find the measure of each angle.

Let the measure of one of the supplementary angles be a .

Measure of the other angle is 2 times a .

So, measure of the other angle is 2 a .

If the sum of the measures of two angles is 180 ° , then the angles are supplementary.

So, a + 2 a = 180 °

Simplify.

3 a = 180 °

To isolate a , divide both sides of the equation by 3 .

3 a 3 = 180 ° 3         a = 60 °

The measure of the second angle is,

2 a = 2 × 60 °               = 120 °

So, the measures of the two supplementary angles are 60 ° and 120 ° .

Example 2:

Find m ∠ P     and     m ∠ Q if ∠ P     and     ∠ Q are supplementary, m ∠ P = 2 x + 15 , and m ∠ Q = 5 x − 38 .

The sum of the measures of two supplementary angles is 180 ° .

So, m ∠ P + m ∠ Q = 180 °

Substitute 2 x + 15 for m ∠ P and 5 x − 38 for m ∠ Q .

2 x + 15 + 5 x − 38 = 180 °

Combine the like terms. We get:

7 x − 23 = 180 °

Add 23 to both the sides. We get:

7 x = 203 °

Divide both the sides by 7 .

7 x 7 = 203 ° 7

Simplify.

x = 29 °

To find m ∠ P , substitute 29 for x in 2 x + 15 .

2 ( 29 ) + 15 = 58 + 15

Simplify.

58 + 15 = 73

So, m ∠ P = 73 ° .

To find m ∠ Q , substitute 29 for x in 5 x − 38 .

5 ( 29 ) − 38 = 145 − 38

Simplify.

145 − 38 = 107

So, m ∠ Q = 107 ° .

See also complementary angles .

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180-x-x=80 -2x=-100 x=50 180-50=130 Hence, the messure of the larger angle is 130 degrees. Paul.