One angle in a triangle is 10 degrees more than the smallest angle in the triangle, whereas the other angle is 20 degrees more than the smallest angle. find the measure of the three angles.

In a triangle, the three interior angles always add to 180°

Three angles of a triangle are x, (x+10) and (x+20)

x + x+10 + x+20 = 180
3x + 30 = 180
3x = 180 - 30
3x = 150
x = 150/3
x = 50°   ←  smallest angle

second angle = x + 10 = 50 + 10 = 60°

third angle = x + 20 = 50 + 20 = 70°

50°, 60° and 70°