Question

one angle of an isosceles triangle measures 110°. what measures are possible for the other two angles? choose all that apply. 110° 40° 35° 15°

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180°. In an isosceles triangle, two angles are equal.

Step2: Determine the type of the given angle

The given angle of 110° cannot be one of the equal - angles. Because if it were, the sum of just two of those angles would be 110°+110° = 220°>180°, which is not possible for a triangle.

Step3: Calculate the measure of the equal angles

Let the measure of each of the equal angles be \(x\). Then, using the angle - sum property of a triangle, we have \(110^{\circ}+x + x=180^{\circ}\). Combining like terms gives \(110^{\circ}+2x = 180^{\circ}\). Subtract 110° from both sides: \(2x=180^{\circ}-110^{\circ}=70^{\circ}\). Divide both sides by 2: \(x = 35^{\circ}\).

Answer:

C. 35°