Supplementary angle space two angles whose measures include up come 180 ° .

The 2 angles that a linear pair , choose ∠ 1     and also     ∠ 2 in the number below, are always supplementary.

But, 2 angles need not be adjacent to it is in supplementary. In the following figure, ∠ 3     and     ∠ 4 are supplementary, since their measures include to 180 ° .

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example 1:

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

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

measure of the various other angle is 2 time a .

So, measure of the other angle is 2 a .

If the sum of the steps of 2 angles is 180 ° , then the angles are supplementary.

So, a + 2 a = 180 °

Simplify.

3 a = 180 °

To isolation a , division both sides of the equation by 3 .

3 a 3 = 180 ° 3         a = 60 °

The measure up of the 2nd angle is,

2 a = 2 × 60 °               = 120 °

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

instance 2:

uncover m ∠ ns     and also     m ∠ Q if ∠ ns     and     ∠ Q space 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 °

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

2 x + 15 + 5 x − 38 = 180 °

combine the prefer terms. Us get:

7 x − 23 = 180 °

add 23 come both the sides. Us get:

7 x = 203 °

divide both the sides by 7 .

7 x 7 = 203 ° 7

Simplify.

x = 29 °

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

2 ( 29 ) + 15 = 58 + 15

Simplify.

58 + 15 = 73

So, m ∠ p = 73 ° .

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