Question

The figure is not drawn to scale. MN, PQ are straight lines. If Zp is four times as large as Zr, what is the sum of Zq and Lr?

A) Zq + Lr
B) 2(Zq + Lr)
C) Zq - Lr
D) 5(Zq + Lr)

Answer 1

The sum of Zq and Lr is 0.

Step-by-step explanation:

To find the sum of Zq and Lr, we need to first determine the values of Zq and Lr. Based on the given information, we know that Zp is four times as large as Zr. Let's assume Zr to be x. Therefore, Zp is 4x.

Since Zp and Zr are alternate interior angles, they are congruent. So, Zp is equal to Zr. Therefore, 4x = x, which gives us x = 0.

Now, we can find the value of Zq. Since Zr = x = 0, Zq is also 0. Similarly, we can find the value of Lr. Since Zr is a right angle, Lr is also 0.

Therefore, the sum of Zq and Lr is 0 + 0 = 0.