Find missing angles in triangles using ratios

Question

One angle of a triangle measures 75°. The other two angles are in a ratio of 4:17. What are the measures of those two angles?

Answer 1

A = 85

A+B+C = 180

B+C = 180-75 = 105

B:C = 4:17

B/C = 4/17

4C = 17B

C = 17B/4

B + 17B/4 = 105

21B/4 = 105

B = (4/21)(105) = 20 degrees

C = (17/4)(20 = 85 degrees