Question

if an isosceles triangle has a base angle measuring 40°, then what measure is the vertex angle?

Explanation:

Step1: Recall the property of isosceles triangle

In an isosceles triangle, the base angles are equal.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the vertex angle be \(x\). Then \(x + 40^{\circ}+40^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

\(x=180^{\circ}-(40^{\circ} + 40^{\circ})=100^{\circ}\)

Answer:

\(100^{\circ}\)