Question

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

Explanation:

Step1: Analyze angle types (obtuse/acute)

An obtuse angle is greater than \(90^\circ\). Here, \(116^\circ>90^\circ\), so the triangle is obtuse. Acute angles are less than \(90^\circ\), but since there's an obtuse angle, it's not acute.

Step2: Analyze side types (isosceles/scalene)

In a triangle, equal angles correspond to equal sides. Two angles are \(32^\circ\), so the sides opposite them are equal. Thus, the triangle has at least two equal sides, making it isosceles (not scalene, as scalene has all sides different).

Answer:

an obtuse isosceles triangle