Question

the vertex angle of an isosceles triangle measures 40°. what is the measure of a base angle? 100° 140° 40° 70°

Explanation:

Step1: Recall the properties of isosceles triangles

In an isosceles triangle, the base angles are equal. Let the measure of each base angle be \(x\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(x + x+40^{\circ}=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(2x+40^{\circ}=180^{\circ}\).
Subtract \(40^{\circ}\) from both sides: \(2x = 180^{\circ}- 40^{\circ}=140^{\circ}\).
Divide both sides by \(2\): \(x=\frac{140^{\circ}}{2}=70^{\circ}\).

Answer:

\(70^{\circ}\)