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Two supplementary angles are in the ratio 2:7. Find the measure of the Acute angle.

Two supplementary angles are in the ratio 2:7. Find the measure of the Acute angle-example-1

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Answer:

y=42.3333333333 (repeating)

Explanation:

You need to find the corresponding side. You can see D H is corresponding to E C. So here is what you have to do, find x to (8x - 43) and (2x + 13).

2x + 13 + 8x - 43= 90

10x -30 = 90

+30 +30

10x = 120

/10 /10 = 12

to check if this is right take x which is 12 and plug it in.

8 x 12= 96 then 96 - 43= 53

2 x 21= 24 then 24 + 13= 37

Next you take 53 and 37 and add it together

53 + 37= 90

about that corresponding side, now you know D H and E C both equal 53

Now you can solve your equation.

53 + 2y + y= 180

53 + 3y = 180

-53 -53

3y = 127

/3 /3

y = 42.333333 (repeating)

to check if this is right take y which is 42.3333333 (repeating) and plug it in.

2y means to multiply y two times so...

42.3333333 (repeating)+ 42.33333333 (repeating)= 84.6666666 (repeating)

y = 42.333333333 (repeating)

E C = 53

add all the numbers together

42.333333 (repeating) + 84.66666666 (repating)+ 53= 180

Therefore y equals 42.33333333 (repeating)

User Danil Speransky
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