Skill: Apply the triangle angle-sum relationship

Every triangle has three interior angles that add to $180^\circ$:

$$\text{angle}_1+\text{angle}_2+\text{angle}_3=180^\circ$$

The triangle’s size, shape, or orientation does not change this relationship. Focus on the angle measures inside the triangle, not the side lengths.

Example: Find the unknown angle $x$.

The two known interior angles measure $52^\circ$ and $67^\circ$.

1. Write an equation using the triangle angle-sum relationship:

$$52^\circ+67^\circ+x=180^\circ$$

2. Add the known angles:

$$119^\circ+x=180^\circ$$

3. Subtract $119^\circ$ from both sides:

$$x=61^\circ$$

4. Check the answer:

$$52^\circ+67^\circ+61^\circ=180^\circ$$

Therefore, the unknown interior angle is $\boxed{61^\circ}$.