Skill: Find unknown angles on a straight line

When adjacent angles lie on a straight line, their measures add up to $180^\circ$.

Example

In the diagram, three adjacent angles form a straight line:

        47°   x°   68°
─────────╱────╱────╱────────

Find $x$.

1. Since the angles form a straight line, their total is $180^\circ$:

$$47^\circ+x+68^\circ=180^\circ$$

2. Add the known angles:

$$47^\circ+68^\circ=115^\circ$$

3. Subtract the known total from $180^\circ$:

$$x=180^\circ-115^\circ$$

4. Calculate:

$$x=65^\circ$$

So, the unknown angle is $\boxed{65^\circ}$. Check: $47^\circ+65^\circ+68^\circ=180^\circ$.