Which geometric figure has two equal angles opposite two equal sides, with the third angle distinct from the other two?

• A. Equilateral
• B. Scalene
• C. Isosceles
• D. Right

Answer: (C)

In any triangle, equal angles sit opposite equal sides, and vice versa. So if two angles are equal, the sides opposite them are equal as well. If those two equal angles correspond to two equal sides and the third angle is different, you have a shape where two sides are the same and the two angles opposite them are the same, with a distinct third angle. That description matches an isosceles triangle. The third angle being different from the equal ones rules out the equilateral case (where all three angles would be the same), and the specific mention of two equal angles opposite two equal sides fits the defining property of an isosceles triangle.