What is the measure of the largest angle if the ratio of the measures of two supplementary angles is 3 7?

Question 8 Revision Exercise

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Answer:

Solution: Ratio between two supplementary angles are= 7:5

Sum of ratios = 7+5=12

But sum of supplementary angles= 180°

First angle= 180° x \frac{7}{12}= 15° x 7=105°

and second angle = \frac{180\times5}{12}= 15 x 15= 75°

Two supplementary angles are 105° and 75°

Video transcript

"Hello, welcome to lido today we're going to see a question that is to supplementary angles and the ratio seven is to find find the angles so they are in the ratio of survival. Where is to find we're going to find the tangle it's to it. So first we need to find out what is the supplementary angles when supplementary made? Hello, welcome to your new home at clay get going to see a question that is to supplementary angles and the ratio 7 is to find find the angles. So they are in the ratio of surveys to find. We're going to find the tangle. It's to it. So first we need to find out what is the supplement trying to spend supplementary means the addition of the triangle is going to be 180 degrees. Supplementary Addition of two angles is 180 degrees. So it is given that it is a ratio. So very strike two angles and ratios on it when you're going to find the angle so should take as 7x plus Phi x equal to 180. Okay, so then what to do next so on X by X is 2x squared to 180. So x equals to 180 by 2 L is 180 by 2 L and take it out and do the division partner of first or 80 divided by 12 kill one jar 12. People fighter 60 so it will be 15 x so x value equals 215. So now put this value x value in this each terms and find out the each angle. So 7 into X. This is the first angle X so server into 15. So answer will be. 105 and then the other angle is Fi L 2X. Clean 215 Pfizer 75, so on the server 105 n 75 I hope you understand this video and thanks for watching this video. "

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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 2 a .

If the sum of the measures 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 by 3 .

3 a 3 = 180 ° 3         a = 60 °

The measure of the second angle is,

2 a = 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 = 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 °

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

2 x + 15 + 5 x − 38 = 180 °

Combine the like terms. We get:

7 x − 23 = 180 °

Add 23 to both the sides. We get:

7 x = 203 °

Divide both the sides by 7 .

7 x 7 = 203 ° 7

Simplify.

x = 29 °

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

2 ( 29 ) + 15 = 58 + 15

Simplify.

58 + 15 = 73

So, m ∠ P = 73 ° .

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

5 ( 29 ) − 38 = 145 − 38

Simplify.

145 − 38 = 107

So, m ∠ Q = 107 ° .

See also complementary angles .

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Two supplementary angles are in the ratio 3:7. Find the angles ? Let the two angles be 3x and 7x. Supplementary angles add up to 180 degrees. Therefore: 3x + 7x = 180 10x = 180 x = 18 3x = 3 * 18 = 54 7x = 7 * 18 = 126 Answer: The two angles are 54 degrees and 126 degrees. Lennox Obuong Algebra Tutor Nairobi, Kenya

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