Question

one angle of an isosceles triangle measures 100°. what measures are possible for the other two angles? choose all that apply. 10° 40° 100° 50°

Explanation:

Step1: Recall triangle - angle sum property

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

Step2: Analyze the given angle

Since the given angle is 100°, it cannot be one of the two equal angles in an isosceles triangle (because if there were two 100° angles, the sum of those two angles alone would be 200° which is greater than 180°).

Step3: Calculate the equal - angle measure

Let the measure of each of the equal angles be \(x\). Then, using the angle - sum property of a triangle, we have \(100 + x+x=180\). Simplifying the left - hand side gives \(100 + 2x=180\). Subtract 100 from both sides: \(2x=180 - 100=80\). Divide both sides by 2: \(x = 40\).

Answer:

B. 40°