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):
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
