Supplementary angles room two angles who measures include up to 180 ° .

The 2 angles of a straight pair , like ∠ 1     and     ∠ 2 in the number below, are constantly supplementary.

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

You are watching: If two angles are supplementary and one of them is 30° what is the measurement of the second angle

instance 1:

2 angles room supplementary. If the measure of the angle is double the measure of the other, discover the measure of every angle.

allow the measure of one of the supplementary angle be a .

measure of the other angle is 2 time a .

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

If the sum of the measures of 2 angles is 180 ° , climate the angles room supplementary.

So, a + 2 a = 180 °

Simplify.

3 a = 180 °

To isolation a , divide both political parties of the equation through 3 .

3 a 3 = 180 ° 3         a = 60 °

The measure up of the 2nd angle is,

2 a = 2 × 60 °               = 120 °

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

example 2:

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

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

So, m ∠ p + m ∠ Q = 180 °

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

2 x + 15 + 5 x − 38 = 180 °

incorporate the favor terms. Us get:

7 x − 23 = 180 °

include 23 come both the sides. Us get:

7 x = 203 °

division both the political parties by 7 .

7 x 7 = 203 ° 7

Simplify.

x = 29 °

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

2 ( 29 ) + 15 = 58 + 15

Simplify.

58 + 15 = 73

So, m ∠ ns = 73 ° .

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