Question

∠C and ∠D are vertical angles.

Answer 1

Vertical angles is the same angle, but we don't know "x". If you look in a way. We can do 180=(3x+80).

100=3x

100/3 = x

Now we have the answer for x we plug it in to get the answer.

3(100/3) + 80 =<D

<D = <C

Answer 2

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

$m\angle C=m\angle D\\\\\Rightarrow x^\circ=(-3x+80^\circ)\\\\\Rightarrow x=-3x+80\\\\\Rightarrow x+3x=80\\\\\Rightarrow 4x=80\\\\\Rightarrow x=\dfrac{80}{4}\\\\\Rightarrow x=20.$

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