Question

an isosceles triangle has an angle that measures 100°. what measures are possible for the other two angles? choose all that apply. 80° 30° 40° 70°

Explanation:

Step1: Recall triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\).

Step2: Analyze the given angle

Since the triangle is isosceles and one angle is \(100^{\circ}\), this \(100^{\circ}\) angle must be the vertex angle (because if it were a base angle, the sum of angles would exceed \(180^{\circ}\)). Let the base angles be \(x\).
Using the angle - sum formula \(100 + 2x=180\).

Step3: Solve for \(x\)

Subtract \(100\) from both sides: \(2x = 180 - 100=80\).
Divide both sides by \(2\): \(x = 40^{\circ}\).

Answer:

\(40^{\circ}\)