Question

an isosceles triangle has an angle that measures 50°. what measures are possible for the other two angles? choose all that apply. 30° 80° 65° 50°

Explanation:

Step1: Case 1: \(50^{\circ}\) is the vertex angle

Sum of angles in a triangle is \(180^{\circ}\).
Let the base angles be \(x\).
Using the property of isosceles triangle (base angles are equal), \(x + x+50^{\circ}=180^{\circ}\)
\(2x=180^{\circ}- 50^{\circ}\)
\(2x = 130^{\circ}\)
\(x = 65^{\circ}\)

Step2: Case 2: \(50^{\circ}\) is a base angle

Let the vertex angle be \(y\).
\(50^{\circ}+50^{\circ}+y = 180^{\circ}\)
\(y=180^{\circ}-(50^{\circ}+50^{\circ})\)
\(y = 80^{\circ}\)

Answer:

\(65^{\circ}\), \(80^{\circ}\), \(50^{\circ}\)