Let's denote the measure of the two equal angles as $x$.

According to the problem:

• The third angle is 30 degrees greater than each of the equal angles, so the measure of the third angle is $x + 30^\circ$.

In a triangle, the sum of all angles is always 180 degrees, so we can write the equation:

$x + x + (x + 30) = 180$

Simplify the equation:

$3x + 30 = 180$

Now, subtract 30 from both sides:

$3x = 150$

Next, divide by 3:

$x = 50$

So, the measure of the two equal angles is 50 degrees. The third angle, which is the largest, is:

$x + 30 = 50 + 30 = 80^\circ$

Thus, the measure of the largest angle is 80 degrees.

Would you like more details on how this was solved, or do you have any other questions?

Here are some related questions you might find helpful:

1. What are the properties of an isosceles triangle?
2. Can a triangle have more than one obtuse angle?
3. How do we find angles of a triangle if given their ratio?
4. What is the sum of angles in any polygon?
5. How do we solve for angles in a right triangle?

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