Question

the vertex angle of an isosceles triangle measures $40^{circ}$. what is the measure of a base angle? $140^{circ}$ $70^{circ}$ $100^{circ}$ $40^{circ}$

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). For an isosceles triangle, the two base angles are equal. Let each base angle be \(x\).

Step2: Set up the equation

The vertex angle is \(40^\circ\), so the equation is \(40^\circ + x + x = 180^\circ\), which simplifies to \(40^\circ + 2x = 180^\circ\).

Step3: Solve for \(x\)

Subtract \(40^\circ\) from both sides: \(2x = 180^\circ - 40^\circ = 140^\circ\). Then divide by 2: \(x=\frac{140^\circ}{2}=70^\circ\).

Answer:

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