Answer:
measure of angle 4 is 140°
measure of angle 1 is 140° (given)
measure of angle 3 is 40°
measure of angle 2 is 40°
Explanation:
We're given that one angle is equal to the measure of 140° (we'll make this one be angle 1)
because of vertical angles theorem, which states that angles that are opposite to each other and are formed by two intersecting lines will be congruent.
So that means that measure of angle 4 will also be 140°
Because of vertical angles theorem, that means that <3 is ≅ to <2 (we can make them be x)
The sum of all the angles will equal to 360° (since it's a full angle)
Here's the equation:
140+140+x+x=360
simplify
280+2x=360
2x=80
x=40°
Which means that <3 and <2 both equal 40°
Hope this helps!