Transversal t cuts parallel lines r and s as shown in the diagram. which theorem does the diagram illustrate?

a) alternate interior angles theorem

b) alternate exterior angles theorem

c) same-side interior angles theorem

d) corresponding angles theorem

The correct option is B. Alternate Exterior angles theorem

Step-by-step explanation:

Let name the marked angles in the figure as x and y

Given that : x = y

So, to state which theorem does the diagram illustrate, we first need to find the relation between the angles x and y

Alternate interior angles : The angles which lie interior to the parallel sides but on the opposite side of the transversal.

But x and y lie exterior to the parallel lines, So this option is rejected.

Alternate exterior angles : The angles which lie exterior to the parallel sides but on the opposite side of the transversal.

But x and y lie exterior to the parallel lines, So this option is correct.

Same side interior angles theorem : This theorem states that the sum of same side interior angles in 180.

So it can't be said angle x = angle y by using this theorem. So, this option is rejected

Corresponding angles theorem : The angle which lie at same relative position of the transversal.

But, angle x and angle y lie on the opposite side. So, this option is rejected

Hence, The correct option is B. Alternate Exterior angles theorem

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions