Question

what kind of triangle is this?
equilateral
isosceles but not equilateral
scalene

Explanation:

Step1: Recall triangle classification rules

• An equilateral triangle has all three angles equal to \(60^{\circ}\).
• An isosceles triangle has at least two equal angles.
• A scalene triangle has all angles different.

Step2: Analyze given angles

The given angles are \(39^{\circ}\), \(102^{\circ}\), and \(39^{\circ}\). There are two equal angles (\(39^{\circ}\) and \(39^{\circ}\)), so it is not scalene (eliminates scalene option). Also, not all angles are \(60^{\circ}\) (eliminates equilateral option).

Answer:

isosceles but not equilateral