The measure of one of the interior angles of an isosceles triangle is 76°. What could be the measure, in degrees, of one of the other interior angles of the triangle?

Sure, let's solve this step by step.

1. Identify the properties of an isosceles triangle:

   • An isosceles triangle has two equal sides, and the angles opposite these sides are also equal.

2. Given information:

   • One of the interior angles is 76°.

3. Determine the possible positions of the 76° angle:

   • The 76° angle can either be one of the two equal angles or the unique angle.

4. Case 1: 76° is one of the two equal angles:

   • Let the other equal angle also be 76°.
   • The sum of the angles in any triangle is 180°.
   • Therefore, the third angle = 180° - 76° - 76° = 180° - 152° = 28°.

5. Case 2: 76° is the unique angle:

   • Let the two equal angles be x.
   • The sum of the angles in any triangle is 180°.
   • Therefore, 76° + x + x = 180°.
   • Simplify to find x: 2x = 180° - 76° = 104°.
   • x = 104° / 2 = 52°.

6. Conclusion:

   • The measures of the other interior angles could be 28° or 52°.