Question

one angle of an isosceles triangle measures 120°. what measures are possible for the other two angles? choose all that apply. 40° 20° 30° 70°

Explanation:

Step1: Analyze the property of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In an isosceles triangle, two angles are equal.

Step2: Determine the nature of the \(120^{\circ}\) angle

Since \(120^{\circ}>90^{\circ}\), it must be the vertex angle (because if it were a base angle, the sum of two \(120^{\circ}\) angles would be \(120^{\circ}+120^{\circ} = 240^{\circ}>180^{\circ}\), which is impossible for a triangle).

Step3: Calculate the base angles

Let the base angles be \(x\). Using the angle - sum formula \(120^{\circ}+2x=180^{\circ}\).
Solve for \(x\):

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Answer:

C. \(30^{\circ}\)