Question

one angle of an isosceles triangle measures 140°. what measures are possible for the other two angles? choose all that apply. 70° 20° 50° 10°

Explanation:

Step1: Analyze the property of angles in a triangle

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

Step2: Determine if \(140^{\circ}\) is the vertex angle

Since \(140^{\circ}+140^{\circ}=280^{\circ}>180^{\circ}\), \(140^{\circ}\) must be the vertex angle.

Step3: Calculate the base angles

Let the base angles be \(x\). Using the angle - sum property \(140 + 2x=180\).
Subtract \(140\) from both sides: \(2x = 180 - 140=40\).
Divide by \(2\): \(x=\frac{40}{2}=20^{\circ}\)

Answer:

\(20^{\circ}\)