Exercise 47 Page 528

We have been given the measures of ∠ ABE and ∠ EBC. Let's add these to the given isosceles trapezoid ABCD.

Recall that if a quadrilateral is an isosceles trapezoid, then each pair of leg angles are supplementary. Therefore, the measures of ∠ ABC and ∠ BCD sum to 180^(∘). The measure of ∠ ABC is the sum of ∠ ABE and ∠ EBC.

40^(∘)+ 35^(∘)= 75^(∘) Let's add this to the diagram.

By setting the sum of ∠ ABC and m∠ BCD equal to 180^(∘), we can solve for m∠ BCD after we substitute the known measure for ∠ ABC.

m∠ ABC + m∠ BCD = 180^(∘)

Substitute

m∠ ABC= 75^(∘)

75^(∘)+m∠ BCD = 180^(∘)

SubEqn

LHS-75^(∘)=RHS-75^(∘)

m∠ BCD=105^(∘)