Final answer:
To solve for x, we apply the triangle sum theorem, which states the sum of the angles in a triangle is 180 degrees. Solving the resultant equation, we find x is approximately 16.67. Substituting back, we determine angle C is approximately 43.34 degrees.
Step-by-step explanation:
The given angles in the question suggest we are dealing with a triangle and need to find the value of x. By the triangle sum theorem, the sum of the interior angles of a triangle is 180 degrees. Since it is not an isosceles triangle, we can assume all angles are different and thus we should have:
Angle A + Angle B + Angle C = 180 degrees
(3x + 20) + (4x) + (2x + 10) = 180
(3x + 4x + 2x) + (20 + 10) = 180
(9x) + 30 = 180
9x = 180 - 30
9x = 150
x = 150 / 9
x = 16.67 (approx)
To find the measure of angle C, we substitute x into its expression:
Angle C = 2x + 10
Angle C = (2 * 16.67) + 10
Angle C = 33.34 + 10
Angle C = 43.34 degrees (approx)