Question

an isosceles triangle has an angle that measures 106°. what measures are possible for the other two angles? choose all that apply. 86° 37° 106° 68°

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.
Since the given angle 106° is an obtuse angle, it cannot be one of the two equal angles. Let the measure of each of the equal angles be \(x\).

Step2: Set up an equation

We know that \(106^{\circ}+x + x=180^{\circ}\), which simplifies to \(106^{\circ}+2x = 180^{\circ}\).
Subtract 106° from both sides: \(2x=180^{\circ}- 106^{\circ}=74^{\circ}\).
Then divide both sides by 2: \(x = \frac{74^{\circ}}{2}=37^{\circ}\).

Answer:

37°