SOLUTION: One angle of a trapezoid measures 10˚ greater than the smallest angle; a third angle measures five times the smallest angle; and the fourth angle measures 20˚ greater tha
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Question 271025: One angle of a trapezoid measures 10˚ greater than the smallest angle; a third angle measures five times the smallest angle; and the fourth angle measures 20˚ greater than four times the smallest angle. Find the measure of the four angles.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
One angle of a trapezoid measures 10˚ greater than the smallest angle
translates as
(i) x = s + 10
a third angle measures five times the smallest angle
translates as
(ii) y = 5s
the fourth angle measures 20˚ greater than four times the smallest angle
translates as
(iii) z = 4s + 20
The sum of all angles is
(iv) S + x+ y + z = 360
by substitution of (i), (ii) and (iii) into (iv), we get
(v) s + s + 10 + 5s + 4s + 20 = 360
combine like terms to get
(v) 11s + 30 = 360
subtract 30 to get
(vi) 11s = 330
divide by 11 to get
s = 30
This means that
x = 40
y = 150
z = 140
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