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
![m\angle C=m\angle D\\\\\Rightarrow x^\circ=(-3x+80^\circ)\\\\\Rightarrow x=-3x+80\\\\\Rightarrow x+3x=80\\\\\Rightarrow 4x=80\\\\\Rightarrow x=\dfrac{80}{4}\\\\\Rightarrow x=20.](/tpl/images/0498/7414/cdf8f.png)
Thus, the required measure of angle C is 20°.