A triangle has one angle of 120 degrees and two equal angles. What is the measure of each of the equal angles?30 degrees90 degrees45 degrees60 degrees

1. ### Break Down the Problem

We have a triangle with one angle measuring $120^\circ$ and two equal angles. We need to find the measure of each of the equal angles.

2. ### Relevant Concepts

The sum of all angles in a triangle is $180^\circ$. If one angle is $120^\circ$, we can denote the two equal angles as $x$. The equation can be set up as:

$120^\circ + x + x = 180^\circ$

This simplifies to:

$120^\circ + 2x = 180^\circ$

3. ### Analysis and Detail

1. Start by isolating $2x$:

$2x = 180^\circ - 120^\circ$ $2x = 60^\circ$

2. Now, solve for $x$:

$x = \frac{60^\circ}{2}$ $x = 30^\circ$

4. ### Verify and Summarize

Let's verify it by checking the sum of all angles:

$120^\circ + 30^\circ + 30^\circ = 180^\circ$

Thus, the calculations are correct, and each of the equal angles measures $30^\circ$.

Final Answer

Each of the equal angles measures $30^\circ$.