Question

problem 11: (first taught in lesson 30) find the measures of the angles of an isosceles obtuse triangle with one angle that is 32°. after you enter your answer press go. go

Explanation:

Step1: Determine if the \(32^{\circ}\) angle is the vertex angle

In an isosceles triangle, the base angles are equal. The sum of angles in a triangle is \(180^{\circ}\). If \(32^{\circ}\) is the vertex angle, then the base angles would be \(\frac{180 - 32}{2}=74^{\circ}\). But \(74^{\circ}\) is acute, and we need an obtuse triangle. So \(32^{\circ}\) must be a base angle.

Step2: Calculate the vertex angle

Since \(32^{\circ}\) is a base angle (and there are two base angles in an isosceles triangle), the vertex angle is \(180-(32 + 32)=116^{\circ}\)

Answer:

\(32^{\circ},32^{\circ},116^{\circ}\)