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^circ ) angle, as shown in the model.
what is the measure of the two congruent angles where the roof pieces meet the walls?
( mangle abc = mangle edc = square^circ )

Explanation:

Step1: Find total interior angle sum

The formula for the sum of interior angles of an $n$-sided polygon is $(n-2)\times180^\circ$. For a pentagon ($n=5$):
$$(5-2)\times180^\circ = 540^\circ$$

Step2: Sum of known angles

Angles at A and E are right angles ($90^\circ$ each), angle at C is $52^\circ$:
$$90^\circ + 90^\circ + 52^\circ = 232^\circ$$

Step3: Calculate sum of congruent angles

Subtract known sum from total sum:
$$540^\circ - 232^\circ = 308^\circ$$

Step4: Find each congruent angle

Divide the remaining sum by 2 (since angles are congruent):
$$\frac{308^\circ}{2} = 154^\circ$$

Answer:

$154$