Answer: The required measure of angle C is 20°.
Step-by-step explanation: Given that ∠C and ∠D are vertical angles, where
m∠C=x° and m∠D=(−3x+80)°.
We are to find the measure of angle C.
We know that the measures of two vertical angles are equal.
So, according to the given information, we must have

Thus, the required measure of angle C is 20°.