Question

your uncle bob is a bricklayer who was given the job of building a brick wall around a garden that is shaped like a regular triangle. however, he wasnt sure how to make the exterior angles (∠a, ∠b, and ∠c) just right. use the polygon exterior angle sum theorem to calculate the measures of the angles.

m∠a=

m∠b=

m∠c=

Explanation:

Step1: Recall the Polygon Exterior Angle Sum Theorem

The sum of the exterior angles of any polygon is \(360^{\circ}\).

Step2: Use the property of a regular triangle

A regular triangle (equilateral triangle) has 3 equal exterior angles. Let \(x\) be the measure of each exterior angle (\(\angle A=\angle B = \angle C=x\)).
So, \(x + x+x=360^{\circ}\), which simplifies to \(3x = 360^{\circ}\).

Step3: Solve for \(x\)

Divide both sides of the equation \(3x = 360^{\circ}\) by 3. We get \(x=\frac{360^{\circ}}{3}=120^{\circ}\).

Answer:

\(m\angle A = 120^{\circ}\)
\(m\angle B = 120^{\circ}\)
\(m\angle C = 120^{\circ}\)