A carpenter is building a frame. Which values of a and b will ensure that the sides of the finished frame are parallel?

An image of four trapezoids around the edges of a square is shown.· The trapezoids all have their shortest bases on the inside.
· The base angles formed with the longer base of the top trapezoid are both labeled a degree sign.
· The base angles formed with the longer base of the right trapezoid are both labeled b degree sign.
· The base angles formed with the longer base of the bottom trapezoid are both labeled a degree sign.
· The base angles formed with the longer base of the left trapezoid are both labeled b degree sign.
(1 point)
Responses

a = 40 and b = 60
a = 40 and b = 60

a = 45 and b = 50
a = 45 and b = 50

a = 30 and b = 60
a = 30 and b = 60

a = 40 and b = 40

1 answer

The correct answer is: a = 40 and b = 40.

For the sides of the finished frame to be parallel, the corresponding angles between the sides must be equal. In this case, the angles labeled a degree sign must be equal and the angles labeled b degree sign must also be equal. Therefore, a = 40 and b = 40 will ensure that the sides of the frame are parallel.