Let the measures of the two equal angles in the triangle be $x$. Since the sum of the two equal angles is equal to the third angle, the third angle will be $2x$.

In any triangle, the sum of the interior angles is always $180^\circ$. Therefore, we can write the equation:

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

Simplifying this equation:

$4x = 180^\circ$

Now, solving for $x$:

$x = \frac{180^\circ}{4} = 45^\circ$

Thus, the two equal angles are $45^\circ$ each, and the third angle is:

$2x = 2 \times 45^\circ = 90^\circ$

Therefore, the measures of the three interior angles are:

• Two angles of $45^\circ$ each
• One angle of $90^\circ$

This means the triangle is a right-angled triangle.

Would you like more details or have any other questions?

Here are 5 related questions:

1. How do you prove that the sum of the interior angles of a triangle is always 180 degrees?
2. Can a triangle have more than one right angle? Why or why not?
3. What are the properties of an isosceles right triangle?
4. If two angles of a triangle are equal, is the triangle always isosceles?
5. How can you classify a triangle based on its angles and sides?

Tip: In any triangle, the largest angle is always opposite the longest side.