∠1 and ∠2 are supplementary angles. m∠1 is 4y+7 , and m∠2 is 9y+4 . Find m∠2 .

Question

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Answer 1

Because you are given that "∠1 and ∠2 are supplementary angles", you can say that the measure of angle 1 added the the measure of angle 2 is equal to 180° or:

m∠1 + m∠2 = 180

Since you are also given that m∠1 = 4y + 7 and m∠2 = 9y + 4, you can substitute "4y + 7" in for "m∠1" and "9y + 4" in for "m∠2":

m∠1 + m∠2 = 180

(4y + 7) + (9y + 4) = 180

Now, drop the parenthesis and combine like terms:

4y + 7 + 9y + 4 = 180

13y + 11 = 180

Then subtract 11 from both sides:

13y = 169

Then divide both sides by 13:

y = 13

But, you are being asked what the measure of angle 2 is so just finding the value of "y" is not sufficient. Since m∠2 = 9y + 4 and you now know what "y" is, you can solve:

m∠2 = 9y + 4

m∠2 = 9(13) + 4

m∠2 = 121°

Answer 2

4y+7 + 9y +4 = 180

13y = 180-11= 169

y = 169/13 = 13

9(13) +4 = 117+4

= 121 degrees = angle 2

180-121 = 59 degrees = angle 1

4(13) +7 = 52+7 = 59