Question

CD =1/2AB In quadrilateral ABCD above, AD || BC and CD =1/2AB. What is the measure of angle B? A) 150° B) 135° C) 120° D) 90°​

Answer 1

Since segment AB is double the length of segment CD, the measure of angle B IS: A) 150°.

Based on the information provided above, we can reasonably infer and logically deduce that quadrilateral ABCD represents a trapezoid because two of its side lengths are parallel. Also, it comprises a right angle.

Since lines AD and BC are parallel lines, the sum of the following angles must be supplementary;

m∠A + m∠B = 180°

m∠C + m∠D = 180°

Since segment AB is double the length of segment CD, we can reasonably infer and logically deduce that a 30°-60°-90° right-angled must be formed by segment AB;

m∠B = 90 + 60

m∠B = 150°