Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Recall isosceles triangle property

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

Step3: Set up equation

The vertex angle is \(40^\circ\), so \(40^\circ + x + x = 180^\circ\).

Step4: Solve for \(x\)

Simplify: \(40^\circ + 2x = 180^\circ\). Subtract \(40^\circ\): \(2x = 180^\circ - 40^\circ = 140^\circ\). Divide by 2: \(x = \frac{140^\circ}{2} = 70^\circ\).

Answer:

\(70^\circ\) (corresponding to the option with \(70^\circ\))