In a certain triangle, the measure of the largest angle is 20 degrees more than twice the measure of the smallest angle. Five times the measure of the smallest angle equals the sum of the measures of the other two angles. Find the measures of the three angles.
Let the medium angle be B degrees
the small angle be A degrees
the large angle be C degrees
Then
C = 2 B + 20 ..................X
5 B = A + C ..................Y
Sum of all angles
A + B + C = 180 .............Z
Applying Y in Z
5 B + B = 180
6 B = 180
B = 30
From X C = 2 x 30 + 20 = 60 + 20 = 80
From Y 5 x 30 = A + 80
150 = A + 80
150 - 80 = A = 70
Hence medium angle B = 30 degrees
the small angle A = 70 degrees
the large angle C = 80 degrees
