Question

The isosceles trapezoid is part of an isosceles triangle with 32 Degree vertex angle. What is the measure of an acute base angle of the trapezoid? a)64 b)58 c)74 d) 32

Answer 1

1. Check the picture below. ABC is an isosceles triangle with vertex C, so m(A)=m(B) = a degrees.

2. For ABED to be a trapezoid, DE must be parallel to AB.

3. DE is parallel to AB so the following is true:

m(CAB)=m(CDE)=a degrees as CAB and CDE are alternate interior angles. (angles F)

m(CBA)=m(CED)=a degrees, as CBA and CED are alternate interior angles.

4.
a+a+32=180
2a=148
a= 148/2= 74 (degrees)

5.Answer : C

the measure of an acute base angle of the trapezoid=a=74 degrees