1. The problem states that a triangle has three equal angles, each labeled as $w + 49^\circ$. 2. We know the sum of the interior angles of any triangle is $180^\circ$. 3. Since all three angles are equal, we can write the equation: $$3(w + 49) = 180$$ 4. Distribute the 3: $$3w + 147 = 180$$ 5. Subtract 147 from both sides: $$3w = 180 - 147$$ 6. Simplify the right side: $$3w = 33$$ 7. Divide both sides by 3 to solve for $w$: $$w = \frac{33}{3} = 11$$ 8. Therefore, the value of $w$ is $11^\circ$. 9. Each angle in the triangle is $w + 49 = 11 + 49 = 60^\circ$, confirming the triangle is equilateral.