Question

Which relationship exists between the two angles? What is the value of x? Find the measure of each angle. A) vertical angles; x = 3; 76 degrees; 76 degrees B) alternate exterior angles; x = 5; 116 degrees; 64 degrees C) corresponding angles: x = 7; 156 degrees; 156 degrees D) alternate exterior angles; x = 5; 116 degrees; 116 degrees

Answer 1

The diagram shows angles (20x+16)° and (21x+11)° are alternate exterior angles, hence equal.
.. 20x +16 = 21x +11
.. 5 = x . . . . . . . . . . . . . subtract 20x +11
.. (20*5 +16)° = 116°

Selection D is appropriate.

Answer 2

D) alternate exterior angles; x = 5; 116 degrees; 116 degrees

If the diagram given by derricklawrence is correct, then you will realize that the angles with expressions are alternate exterior angles, so they have the same value, which means that the equations are equal to each other. So we can create the following equality:
21x + 11 = 20x + 16

Now to solve for x. Subtract 20x from both sides, getting:
x + 11 = 16

Subtract 11 from both sides, getting:
x = 5

Now substitute the known value for X into one of the equations.
20x + 16 = d
20*5 + 16 = d
100 + 16 = d
116 = d

And of the available options, choice "D) alternate exterior angles; x = 5; 116 degrees; 116 degrees" is an exact match.