Skill: Determine unknown angles in triangles

The three interior angles of every triangle add to $180^\circ$.

To find an unknown angle:

1. Add the two known angles.
2. Subtract that sum from $180^\circ$.
3. Check that the three angles add to $180^\circ$.

Example: In triangle $ABC$, $\angle A=48^\circ$, $\angle B=67^\circ$, and $\angle C=x^\circ$. Find $x$.

First, write the angle-sum equation:

$$48+67+x=180$$

Add the known angles:

$$115+x=180$$

Subtract $115$ from both sides:

$$x=65$$

So, the unknown angle is

$$\boxed{65^\circ}$$

Check:

$$48^\circ+67^\circ+65^\circ=180^\circ$$

Remember that a drawing may make one angle look larger or smaller, but the markings and given measures—not its appearance—determine the angle measure.