Question

an isosceles triangle has an angle that measures 106°. what measures are possible for the other two angles? choose all that apply. 106° 69° 37° 16°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In an isosceles triangle, two angles are equal.
Let the equal angles be \(x\).
We know that one angle is 106°. Since 106° is an obtuse angle, it cannot be one of the equal angles (because if there were two 106° angles, the sum of those two alone would be \(106^{\circ}+ 106^{\circ}=212^{\circ}>180^{\circ}\)).

Step2: Set up an equation

So, we have the equation \(x + x+106^{\circ}=180^{\circ}\), which simplifies to \(2x=180^{\circ}- 106^{\circ}\).

Step3: Solve for \(x\)

First, calculate \(180 - 106=74^{\circ}\). Then, \(2x = 74^{\circ}\), so \(x=\frac{74^{\circ}}{2}=37^{\circ}\).

Answer:

C. 37°