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
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.
To ensure that the sides of the finished frame are parallel, the base angles formed with the longer base of the top and bottom trapezoids should be equal, and the base angles formed with the longer base of the right and left trapezoids should also be equal.
From the given options, the values that satisfy these conditions are:
a = 40 and b = 60