Exercise 13 Page 508

We are asked to find the measure of ∠EDC using the given information. Let's notice that, since diagonals in a rectangle are congruent and bisect each other, AE=DE. This means that triangle AED is an isosceles triangle and m∠DAE=m∠ADE.

Recall that in a rectangle all four angles are right angles. Therefore, the sum of m∠ADE and m∠EDC is 90.

m∠ADE+m∠EDC=90

Substitute

m∠ADE= 65

65+m∠EDC=90

SubEqn

LHS-65=RHS-65

m∠EDC=25

The measure of ∠EDC is 25.