Question

one angle of an isosceles triangle measures 140°. what measures are possible for the other two angles? choose all that apply. 80° 140° 20° 50°

Explanation:

Step1: Determine the type of angle \(140^{\circ}\)

In an isosceles triangle, the sum of interior angles is \(180^{\circ}\). Since \(140^{\circ}+140^{\circ}=280^{\circ}>180^{\circ}\), the \(140^{\circ}\) angle cannot be one of the two equal angles. So \(140^{\circ}\) is the vertex angle.

Step2: Calculate the measure of the base angles

Let the measure of each base angle be \(x\). Using the angle - sum property of a triangle (\(A + B + C=180^{\circ}\)), where \(A = 140^{\circ}\) and \(B = C=x\). Then \(140^{\circ}+x + x=180^{\circ}\), which simplifies to \(140^{\circ}+2x=180^{\circ}\). Subtract \(140^{\circ}\) from both sides: \(2x=180^{\circ}-140^{\circ}=40^{\circ}\). Divide both sides by 2: \(x = 20^{\circ}\)

Answer:

\(20^{\circ}\)