Question

In isosceles trapezoid ABCD, AD = BC. What is

mLA +mZC?
A. 45
B. 90
C. 180 D. 360

Answer 1

Since AD = BC, we know that angles A and B are congruent, and angles C and D are congruent as well. Let's call the measure of angle A (and angle B) "x," and the measure of angle C (and angle D) "y."

Since ABCD is an isosceles trapezoid, we know that angles A and B add up to 180 degrees, as do angles C and D. Therefore, we have:

x + x + y + y = 180

Simplifying this equation, we get:

2x + 2y = 180

Dividing both sides by 2, we get:

x + y = 90

So the sum of the measures of angles A and C is 90 degrees. Therefore, mLA + mZC = 90 degrees, which corresponds to answer choice (B).