Question

If the measures of two angles are 180° the they are supplement of each other

Answer 1

Answer:

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Step-by-step explanation:

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

Measure of the other angle is 22 times aa .

So, measure of the other angle is 2a2a .

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

So, a+2a=180°a+2a=180°

Simplify.

3a=180°3a=180°

To isolate aa , divide both sides of the equation by 33 .

3a3=180°3    a=60°3a3=180°3    a=60°

The measure of the second angle is,

2a=2×60°       =120°2a=2×60°       =120°

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

Example 2:

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

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

So, m∠P+m∠Q=180°m∠P+m∠Q=180°

Substitute 2x+152x+15 for m∠Pm∠P and 5x−385x−38 for m∠