In triangle ABC, the ratio of the measure of angle A to the measure of angle B is 3:5. The measure of angle C is 20 more than the sum of the measure of angles A and B. What is the measure of each angle in triangle ABC?
B = X deg.
A = 3X/5 deg.
C = X + 3X/5 + 20.
A + B + C = 180 deg.
3X/5 + X + (3X/5+X+20) = 180,
6X/5 + 2X + 20 = 180,
6X/5 + 2X = 180 - 20 = 160,
Multiply both sides by 5:
6X + 10X = 800,
16X = 800,
X = 50 deg = B.
A = 3X/5 = 3*50/5 = 30 deg.
C = 30 + 50 + 20 = 100 deg.