### Home > GC > Chapter 5 > Lesson 5.3.5 > Problem 5-120

trapezoid *ABCD*at right. Homework Help ✎Find the measures of all the angles in the diagram.

What is the sum of the angles that make up the trapezoid

*ABCD*? That is, what is*m∡A*+*m∡ABC*+*m∡BCD*+*m∡D*?

The corresponding angles are equal.

Since line *AB* || line *EC*, then corresponding angles ∠*BAE* = ∠*CED*.

So ∠*CED* = 40°, mark it on your diagram.

While line *CD* || line *EB*, then corresponding angles ∠*CDE* = ∠*BEA*.

So ∠*BEA* = 60°, mark it on your diagram

Use the Triangle Angle Sum Theorem.

Now you know two angles in Δ*ABE* and Δ*CED*, knowing that one angle is 40° and 60° Calculate the third angle using the equation 40° + 60° + missing angle = 180°: So the missing angle is 80°. Mark it in your diagram.

The angles at *E* form a straight angle, which is 180º.

Since ∠*BEA* = 60° and ∠*CED* = 40° then 40° + 60° + ∠*CEB* = 180°.

Solve for ∠*CEB*, mark it on your diagram. ∠*CEB* = 80°.

The alternate interior angles are equal.

Since ∠*BEA* = 60° and ∠*CED* = 40°, then ∠*EBC* = 60° and ∠*ECB* = 40° because alternate angles are equal. Mark the angles on your diagram.

40° + (80° + 60°) + (40° + 80°) + 60° = 360°

Note: Do not add in the angles at *E*.