In the diagram below, line AB is parallel to line CD. The measure of
∠∠ABC is 28° and the measure of ∠∠EDC is 42°. Find the measure of∠∠CED. Explain why you are correct by presenting an informal argument that uses the angle sum of a triangle.

what is the measure of ∠∠CED is ? And Explain why ?

Answer:

ced is 110 degrees

Step-by-step explanation:

because ECD is 28 degrees and 28+42=70 and a triange always = 180 degrees so it would have to be 110

The measure of ∠CED is 110 degrees by angle sum property of the triangle.

We are given that line AB is parallel to line CD.

The measure of ∠ABC is 28° and the measure of ∠EDC is 42°

An exterior angle is a measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended.

We know that line AB is parallel to line CD.

So according to alternate interior angles measure of ∠ABC is 28° will be equal to BCD.

Thus, Angle BCD= 28 degrees

Hence, in a triangle CED

∠CED + ∠EDC + BCD = 180

∠CED + 28 + 42 = 180

∠CED = 180 - 70

∠CED = 110 degrees

Therefore, the measure of ∠CED is 110 degrees by angle sum property of the triangle.

Learn more about interior and exterior angles here:

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