Examine trapezoid $ABCD$ below.  

1. Find the measures of all the angles in the diagram.

   Step 1(a):

   The corresponding angles are equal.

   Answer 1(a):

   Since line $\overline{AB}$ $\Vert$ line $\overline{EC}$, then corresponding angles $∠BAE=∠CED$.
   So $∠CED=40º$, mark it on your diagram.
   While line $\overline{CD}$ $\Vert$ line $\overline{EB}$, then corresponding angles $∠CDE=∠BEA$.
   So $∠BEA=60º$, mark it on your diagram.

   Step 2(a):

   Use the Triangle Angle Sum Theorem.

   Answer 2(a):

   Now you know two angles in $ΔABE$ and $ΔCED$, knowing that one angle is $40º$ and $60º$.
   Calculate the third angle using the equation $40º+60º+\text{missing angle}=180º$.
   So the missing angle is $80º$. Mark it in your diagram.

   Step 3(a):

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

   Answer 3(a):

   Since $∠BEA=60º$ and $∠CED=40º$ then $40º+60º+∠CEB=180º$.
   Solve for $∠CEB$, mark it on your diagram. $∠CEB=80^{\circ}$.

   Step 4(a):

   The alternate interior angles are equal.

   Answer 4(a):

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

   

   

   

   

2. What is the sum of the angles that make up the trapezoid $ABCD$? That is, what is $m∠A+m∠ABC+m∠BCD+m∠D$?

   Answer (b):

   $40º+\left(80º+60º\right)+\left(40º+80º\right)+60º=360º$
   Note: Do not add in the angles at $E$.