Question

type the correct answer in the box
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 =

Explanation:

Step1: Recall the formula for the sum of interior angles of a pentagon

The sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For a pentagon (\(n=5\)), the sum \(S=(5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Substitute the known angles into the sum formula

We know that \(\angle A=\angle E = 90^{\circ}\) and \(\angle C = 52^{\circ}\), and \(\angle ABC=\angle EDC=x\) (let the measure of \(\angle ABC\) and \(\angle EDC\) be \(x\)). Then \(90^{\circ}+90^{\circ}+x + x+52^{\circ}=540^{\circ}\).

Step3: Simplify the equation

Combine like - terms: \(232^{\circ}+2x=540^{\circ}\).
Subtract \(232^{\circ}\) from both sides: \(2x=540^{\circ}-232^{\circ}=308^{\circ}\).
Divide both sides by 2: \(x = 154^{\circ}\).

Answer:

\(154\)