Exercise 48 Page 528

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

In the previous exercise we found measure of ∠ BCD=105^(∘). Let's add this to the diagram.

Recall the Interior Angles Theorem.

Interior Angles Theorem

The sum of the interior angles of triangle is 180^(∘).

Note that sum of interior angles in △ BCD is 180^(∘). ∠ DBC + ∠ BCD + ∠ CDB =180^(∘) Let's substitute the measures of given angles and solve the equation.

∠ DBC + ∠ BCD + ∠ CDB=180^(∘)

SubstituteII

∠ DBC= 35^(∘), ∠ BCD= 105^(∘)

35^(∘) + 105^(∘) + ∠ CDB =180^(∘)

AddTerms

Add terms

140^(∘) + ∠ CDB =180^(∘)

SubEqn

LHS-140^(∘)=RHS-140^(∘)

∠ CDB = 40 ^(∘)