Skill: Determine unknown angles in triangles

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

To find an unknown angle:

1. Identify the three interior angles.
2. Write an equation showing that they add to $180^\circ$.
3. Solve for the unknown.
4. Check that the three angle measures total $180^\circ$.

Example: A triangle has angles measuring $52^\circ$, $67^\circ$, and $x^\circ$. Find $x$.

Step 1: Write the angle-sum equation.

$$52 + 67 + x = 180$$

Step 2: Add the known angles.

$$119 + x = 180$$

Step 3: Subtract $119$ from both sides.

$$x = 180 - 119$$ $$x = 61^\circ$$

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

Check:

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

The answer is correct. Remember that a diagram may not be drawn to scale, so use the given angle measures and angle relationships rather than guessing from the picture. If an angle forms a straight line with another angle, those two angles are supplementary and add to $180^\circ$.