Question

an isosceles triangle has an angle that measures 140°. what measures are possible for the other two angles? choose all that apply. 70° 20° 80° 140°

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180°. In an isosceles triangle, two angles are equal.

Step2: Analyze the given angle

The given angle is 140°. Since the sum of all angles in a triangle is 180°, this 140° angle cannot be one of the two equal angles (because if it were, 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 \(140 + 2x=180\).
Subtract 140 from both sides: \(2x=180 - 140\).
So, \(2x = 40\).
Divide both sides by 2: \(x = 20\).

Answer:

20°