Solving for Triangle Angle C

The sum of the interior angles in any triangle is always $180^\circ$. This fundamental property can be represented by the formula:

$ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ $

Applying the Angle Sum Theorem

We are given the measures of two angles:

• Angle A = $30^\circ$
• Angle B = $45^\circ$

Substitute these values into the formula:

$ 30^\circ + 45^\circ + \text{Angle C} = 180^\circ $

Calculating Angle C

First, sum the known angles:

$ 75^\circ + \text{Angle C} = 180^\circ $

Next, isolate Angle C by subtracting $75^\circ$ from both sides:

$ \text{Angle C} = 180^\circ - 75^\circ $

$ \text{Angle C} = 105^\circ $

Therefore, the measure of angle C is $105^\circ$.