Question

Suppose you are a designer making the traffic sign below.

1. What is the sum of the interior angles of the equilateral triangle?

2. What is the measure of ∠N?

3. What is the measure of ∠M? Explain your reasoning.

4. What is the sum of the exterior angles of the equilateral triangle ∠M + ∠R + ∠X? Explain your reasoning.

Answer 1

Explanation:

The sum of the interior angles is equal to 180 degrees. The measure of angle N is ∠N=60°. The measure of angle M is ∠M=120°. The sum of the the exterior angles is 360°

Answer 2

Part 1) The sum of the interior angles is equal to 180 degrees

Part 2) The measure of angle N is ∠N=60°

Part 3) The measure of angle M is ∠M=120°

Part 4) The sum of the the exterior angles is 360°

Explanation:

Part 1) What is the sum of the interior angles of the equilateral triangle?

we know that

The sum of the interior angles of any triangle must be equal to 180 degrees

Part 2) What is the measure of ∠N?

we know that

An equilateral triangle has three equal sides and three equal internal angles ( each internal angle measure 60 degrees)

so

In this problem

∠N=60°

Part 3) What is the measure of ∠M? Explain your reasoning.

we know that

∠M+∠N=180° -----> by supplementary angles (linear pair)

we have

∠N=60°

substitute

∠M+60°=180°

∠M=180°-60°=120°

Part 4) What is the sum of the exterior angles of the equilateral triangle ∠M + ∠R + ∠X?

we know that

The sum of the the exterior angles of any polygon is equal to 360 degrees

In this problem

we have

∠M=∠R=∠X=120°

so

∠M+∠R+∠X=120°+120°+120°=360°