SOLUTION: The interior angles of the quadrilateral are in the ratio of 1:2:3:4 . Find the measure of each angle.

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Question 1113682: The interior angles of the quadrilateral are in the ratio of 1:2:3:4 . Find the measure of each angle.
Found 2 solutions by Edwin McCravy, amalm06:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
To break a sum up into 4 parts in the ratio a:b:c:d

a:b:c:d = ak:bk:ck:dk where k is not zero.

ak+bk+ck+dk = sum

k(a+b+c+d) = sum

k = sum/(a+b+c+d)

For our problem, a=1, b=2, c=3, d=4

The sum of the four interior angles of a quadrilateral is 360°,
so sum = 360°

k = 360°/(1+2+3+4)

k = 360°/10

k = 36°

ak = 1(36°) = 36°
bk = 2(36°) = 72°
ck = 3(36°) = 108°
dk = 4(36°) = 144°

Edwin
Answer by amalm06(224)   (Show Source): You can put this solution on YOUR website!




x=36°,72°,108°,144° (Answer)
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