Question

an isosceles triangle has an angle that measures 130°. what measures are possible for the other two angles? choose all that apply. 130° 70° 85° 25°

Explanation:

Step1: Analyze the property of the largest angle in a triangle

In a triangle, the sum of interior angles is \(180^{\circ}\). Since \(130^{\circ}+130^{\circ}=260^{\circ}>180^{\circ}\), the \(130^{\circ}\) angle can only be the vertex angle.

Step2: Calculate the measure of the base angles

Let the measure of each base angle be \(x\). Using the angle - sum property of a triangle (\(A + B + C=180^{\circ}\)), where \(A = 130^{\circ}\) (vertex angle) and \(B = C=x\) (base angles of an isosceles triangle).
We have the equation \(130^{\circ}+x + x=180^{\circ}\), which simplifies to \(130^{\circ}+2x=180^{\circ}\).
Subtract \(130^{\circ}\) from both sides: \(2x=180^{\circ}-130^{\circ}=50^{\circ}\).
Divide both sides by 2: \(x = 25^{\circ}\).

Answer:

\(25^{\circ}\)