Applying the vertical angle theorem, the measure of the missing angles are:
e = 31
f = 72
d = 77
What is the Vertical Angle Theorem?
The vertical angles theorem states that two angles that are vertically opposite to each other have equal measures.
Angle e and 31 degrees are vertical angles. Therefore, based on the vertical angles theorem,
e = 31 degrees.
Also, d = 77 degrees [vertical angles theorem].
e + 77 + f = 180 degrees [straight line angles have a sum of 180 degrees].
Substitute the value of e into the equation
31 + 77 + f = 180
108 + f = 180
Subtract 108 from both sides
108 + f - 108 = 180 - 108
f = 72 degrees.
Learn more about the vertical angle theorem on:
https://brainly.com/question/24839702
#SPJ1
