Skill: Find a missing angle in a triangle

The three interior angles inside every triangle add up to $(180^\circ)$.

To find a missing angle:

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

Example

A triangle has angles measuring $(65^\circ)$, $(45^\circ)$, and $(x^\circ)$. Find $x$.

Write an equation using the triangle angle sum:

$$65^\circ + 45^\circ + x^\circ = 180^\circ$$

Add the known angles:

$$110^\circ + x^\circ = 180^\circ$$

Subtract $(110^\circ)$ from both sides:

$$x^\circ = 180^\circ - 110^\circ$$

So,

$$\boxed{x = 70^\circ}$$

Check:

$$65^\circ + 45^\circ + 70^\circ = 180^\circ$$

Therefore, the missing interior angle is $\boxed{70^\circ}$.