Question

an isosceles triangle has an angle that measures 140°. what measures are possible for the other two angles? choose all that apply. 10° 20° 50° 140°

Explanation:

Step1: Analyze the given angle

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

Step2: Calculate the other two angles

Let the measure of each of the other two equal angles be \(x\). Using the angle - sum property of a triangle \(140 + x + x=180\). Simplify the equation: \(140+2x = 180\). Subtract \(140\) from both sides: \(2x=180 - 140=40\). Divide both sides by \(2\): \(x = 20^{\circ}\)

Answer:

\(20^{\circ}\)