Question

6)
architecture in an a-frame house, the roof extends to the ground level. if each side of the roof meets the ground at a 66° angle, what will be the measure of the angle where the two sides of the roof meet?
the angle measure will be ______ °.

Explanation:

Step1: Recall triangle angle sum

A triangle's interior angles sum to \(180^\circ\). The A - frame roof forms an isosceles triangle with the ground, where two base angles are \(66^\circ\) each.

Step2: Calculate the vertex angle

Let the vertex angle (where the two roof sides meet) be \(x\). Using the angle - sum property: \(x + 66^\circ+ 66^\circ=180^\circ\).
Simplify: \(x+132^\circ = 180^\circ\).
Subtract \(132^\circ\) from both sides: \(x = 180^\circ - 132^\circ=48^\circ\).

Answer:

\(48\)