Applying the vertical angle theorem, the measure of the missing angles are:
e = 31
f = 72
d = 77
<h3>What is the Vertical Angle Theorem?</h3>
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.
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