Question

If (m + 7) and (m + 13 )° are spplement of each other, then what is the measure of the larger angle between them?​

Answer 1

Answer:

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 2a .

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

So, a+2a=180°

Simplify.

3a=180°

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

3a3=180°3    a=60°

The measure of the second angle is,

2a=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=2x+15 , and m∠Q=5x−38 .

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

So, m∠P+m∠Q=180°

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

2x+15+5x−38=180°

Combine the like terms. We get:

7x−23=180°

Add 23 to both the sides. We get:

7x=203°

Divide both the sides by 7 .

7x7=203°7

Simplify.

x=29°

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

2(29)+15=58+15

Simplify.

58+15=73

So, m∠P=73° .

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

5(29)−38=145−38

Simplify.

145−38=107

So, m∠Q=107° .

Step-by-step explanation:

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Answer 2

SOLUTION

GIVEN

(m + 7°) and (m + 13° ) are supplement of each other

TO DETERMINE

The measure of the larger angle between them

EVALUATION

Here it is given that (m + 7°) and (m + 13° ) are supplement of each other

We know that two angles are said to be supplementary if sum of angles = 180°

So by the given condition

m + 7° + m + 13° = 180°

⇒ 2m + 20° = 180°

⇒ 2m = 160°

⇒ m = 80°

Thus we have

First angle = m + 7° = 80° + 7° = 87°

Second angle = m + 13° = 80° + 13° = 93°

FINAL ANSWER

The measure of the larger angle between them = 93°

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