1. **Problem Statement:** We are given an equilateral triangle as part of a traffic sign design. We need to find the sum of the interior angles of the equilateral triangle, the measure of angle $\angle N$, and the measure of angle $\angle M$. 2. **Formula and Important Rules:** - The sum of interior angles of any triangle is always $$180^\circ$$. - In an equilateral triangle, all sides are equal, and all interior angles are equal. - Since the triangle is equilateral, each interior angle measures $$\frac{180^\circ}{3} = 60^\circ$$. 3. **Calculations:** - Sum of interior angles of the equilateral triangle: $$\text{Sum} = 180^\circ$$ - Measure of $\angle N$: Since $\angle N$ is one of the interior angles of the equilateral triangle, it measures: $$\angle N = 60^\circ$$ - Measure of $\angle M$: $\angle M$ is also an interior angle of the equilateral triangle, so: $$\angle M = 60^\circ$$ 4. **Explanation:** - The sum of interior angles in any triangle is always 180 degrees. - In an equilateral triangle, all sides and angles are equal. - Therefore, each angle in the equilateral triangle is 60 degrees. - Hence, both $\angle N$ and $\angle M$ measure 60 degrees each. **Final answers:** - Sum of interior angles: $$180^\circ$$ - Measure of $\angle N$: $$60^\circ$$ - Measure of $\angle M$: $$60^\circ$$