These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
The two posters above have solved the question algebraically, so let's use the INPUT-OUTPUT approach.

Let the ORIGINAL angle = 40°

If we keep rotating the lines....

..... we'll eventually get to the point where the angle of intersection = 0°

At this point, the two lines have rotated a total of 40°

From here, we keep rotating the lines....

..... until the angle of intersection is 90°
At this point, the two lines have rotated an additional 90° (starting from when the angle of intersection was 0°)

40° + 90° = 130°
So, the TWO lines have rotated a total of 130°
This means EACH line rotates 65°

So, when we INPUT a starting angle of 40°, the answer to the question (aka the OUTPUT) = 65°

At this point we check each answer choices to see which one yields and output of 65 when we input a starting value \(\theta\) = 40

A. \(90 - 40 = \) 50. NO GOOD. We want an output of 65

B. \(90 - \frac{40}{2}=\) 70. NO GOOD. We want an output of 65

C. \(90 + \frac{40}{2}\) 110. NO GOOD. We want an output of 65

D. \(\frac{90 + 40}{2}\) 65. GREAT!

E. \(\frac{90 + 2(40)}{2}\) 85. NO GOOD. We want an output of 65

Answer: D

Cheers,
Brent