Question

one angle of an isosceles triangle measures 140°. what measures are possible for the other two angles? choose all that apply.
20° 50° 40° 140°

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180°.

Step2: Analyze the given angle

The given angle is 140°. Since an isosceles triangle has two equal - angles, and 140° cannot be one of the equal angles (because if there were two 140° angles, the sum of the angles would be 140°+140° = 280°>180°).

Step3: Calculate the equal angles

Let the measure of each of the equal angles be \(x\). Then, using the angle - sum property of a triangle, we have \(140^{\circ}+x + x=180^{\circ}\). Simplifying the left - hand side gives \(140^{\circ}+2x = 180^{\circ}\). Subtract 140° from both sides: \(2x=180^{\circ}-140^{\circ}=40^{\circ}\). Divide both sides by 2: \(x = 20^{\circ}\).

Answer:

20°