Question

an isosceles triangle has an angle that measures 100°. what measures are possible for the other two angles? choose all that apply. 40° 80° 100° 10°

Explanation:

Step1: Analyze the property of the sum of angles in a triangle

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

Step2: Determine the type of the \(100^{\circ}\) angle

Since \(100^{\circ}> 90^{\circ}\), it must be the vertex angle (because if it were a base angle, the sum of two \(100^{\circ}\) angles would be \(200^{\circ}>180^{\circ}\), which is impossible).

Step3: Calculate the measure of the base angles

Let the measure of each base angle be \(x\). Using the angle - sum formula \(100 + 2x=180\). Solving for \(x\):

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Answer:

\(40^{\circ}\)