Answer:
D. 140°.
Step-by-step explanation:
We have been given an image of two intersecting lines. We are asked to find the measure of angle 3.
We know that when two line intersect they form two pairs of vertical angles.
Since angle 3 and angle 4 are vertical angle, they will be equal in measure. Using this information, we can set an equation as:
[tex]m\angle 3=m\angle 4[/tex]
Upon substituting the expression for angle 3 and angle 4 is our equation we will get:
[tex]x+30=2x-80[/tex]
[tex]x-2x+30=2x-2x-80[/tex]
[tex]-x+30=-80[/tex]
[tex]-x=-110[/tex]
Upon dividing both sides of our equation by -1, we will get:
[tex]\frac{-x}{-1}=\frac{-110}{-1}[/tex]
[tex]x=110[/tex]
Upon substituting [tex]x=110[/tex] in expression for angle 3, we will get:
[tex]m\angle 3=x+30[/tex]
[tex]m\angle 3=110+30[/tex]
[tex]m\angle 3=140[/tex]
Therefore, the measure of angle 3 is 140 degrees and option D is the correct choice.
