Question

what type of triangle can be formed with angle measures of 32°, 116°, and 32°? an obtuse scalene triangle an acute scalene triangle an acute isosceles triangle an obtuse isosceles triangle

Explanation:

1. First, check the angle types: An obtuse angle is greater than \(90^\circ\) and less than \(180^\circ\). Here, \(116^\circ\) is obtuse, so the triangle is obtuse.
2. Then, check side - angle relationship: In a triangle, equal angles correspond to equal sides. Since two angles (\(32^\circ\) and \(32^\circ\)) are equal, the sides opposite these angles are equal. So the triangle is isosceles (a triangle with at least two equal sides).
3. Eliminate other options:

• "an obtuse scalene triangle" is wrong because scalene triangles have all sides (and thus all angles) different, but we have two equal angles here.
• "an acute scalene triangle" and "an acute isosceles triangle" are wrong because the triangle has an obtuse angle (\(116^\circ\)), so it can't be acute.

Answer:

an obtuse isosceles triangle