Supplementary angle room two angle whose measures add up to 180 ° .

The 2 angles of a direct pair , choose ∠ 1     and also     ∠ 2 in the figure below, are constantly supplementary. But, 2 angles need not be adjacent to be supplementary. In the following figure, ∠ 3     and also     ∠ 4 are supplementary, because their measures include to 180 ° . You are watching: Are all supplementary angles linear pairs

instance 1:

2 angles space supplementary. If the measure up of the edge is twice the measure up of the other, find the measure up of each angle.

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

measure up of the other angle is 2 time a .

So, measure up of the other angle is 2 a .

If the sum of the procedures 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 through 3 .

3 a 3 = 180 ° 3         a = 60 °

The measure up of the second angle is,

2 a = 2 × 60 °               = 120 °

So, the procedures of the 2 supplementary angles space 60 ° and 120 ° .

instance 2:

discover m ∠ p     and     m ∠ Q if ∠ ns     and also     ∠ Q space supplementary, m ∠ ns = 2 x + 15 , and m ∠ Q = 5 x − 38 .

The amount of the procedures of 2 supplementary angle is 180 ° .

So, m ∠ ns + m ∠ Q = 180 °

instead of 2 x + 15 because that m ∠ ns and 5 x − 38 because that m ∠ Q .

2 x + 15 + 5 x − 38 = 180 °

incorporate the favor terms. We get:

7 x − 23 = 180 °

include 23 to both the sides. We get:

7 x = 203 °

divide both the political parties by 7 .

7 x 7 = 203 ° 7

Simplify.

x = 29 °

To find m ∠ ns , instead of 29 because that x in 2 x + 15 .

2 ( 29 ) + 15 = 58 + 15

Simplify.

58 + 15 = 73

So, m ∠ p = 73 ° .

See more: Drag The Labels Onto The Diagram To Identify The Structures Or Steps In Protein Synthesis.

To uncover m ∠ Q , instead of 29 because that x in 5 x − 38 .