Question

You are building a dollhouse for your younger sister. The frame is in the shape of a pentagon. You want the two roof pieces to meet at a 52° angle, as shown in the model. What is the measure of the two congruent angles where the roof pieces meet the walls?

m∠ABC = m∠EDC = °

Answer 1

m∠ABC = m∠EDC = 154°

Explanation:

The roof forms and isosceles triangle and the following relationships can be observed:

m∠EDC + m∠ABC = 52 = 180

m∠ABC = m∠EDC = 64.

Since the frame of the walls make a 90 degree angle with the roof, then:

m∠CDB + 90 = m∠EDC

m∠CBD + 90 = m∠ABC

m∠ABC = m∠EDC = 64 + 90

m∠ABC = m∠EDC = 154°