We know: The sum of the measures of the angles of a triangle is equal 180°.
We have: m∠A =65°, m∠B = (3x - 10)° and m∠C = (2x)°.
The equation:
65 + (3x - 10) + 2x = 180
(3x + 2x) + (65 - 10) = 180
5x + 55 = 180 subtract 55 from both sides
5x = 125 divide both sides by 5
x = 25
m∠B = (3x - 10)° → m∠B = (3 · 25 - 10)° = (75 - 10)° = 65°
m∠C = (2x)° → m∠C = (2 · 25)° = 50°
Answer: x = 25, m∠B = 65°, m∠C = 50°