Answer:
The measures of the interior angles are 30 degrees, 30 degrees, and 120 degrees.
Explanation:
In a triangle, the sum of the exterior angles is always 360 degrees. For an isosceles triangle, two of the interior angles are congruent (they have the same measure). Let x be the measure of one of these congruent interior angles.
Since the sum of two exterior angles is given as 240 degrees, the third exterior angle is 360 - 240 = 120 degrees.
Now, the exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles. In this case, the exterior angle is 120 degrees, and one of the non-adjacent interior angles is x. So, the other non-adjacent interior angle is also x.
Therefore, the interior angles of the isosceles triangle are x, x, and 120 degrees.
If you want to find the measure of each interior angle, you can set up an equation:
x + x + 120 = 180 (the sum of interior angles in a triangle is 180 degrees)
Combine like terms:
2x + 120 = 180
Subtract 120 from both sides:
2x = 60
Divide by 2:
x = 30
So, the interior angles of the isosceles triangle are 30 degrees, 30 degrees, and 120 degrees.