Question

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

Explanation:

Step1: Recall the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the vertex angle be \(V = 40^{\circ}\) and the base angles be \(B_1\) and \(B_2\). In an isosceles triangle, \(B_1=B_2\).

Step2: Set up the equation

We know that \(V + B_1 + B_2=180^{\circ}\). Since \(B_1 = B_2\), the equation becomes \(V+2B_1 = 180^{\circ}\).

Step3: Solve for \(B_1\)

Substitute \(V = 40^{\circ}\) into the equation \(40^{\circ}+2B_1=180^{\circ}\).
First, subtract \(40^{\circ}\) from both sides: \(2B_1=180^{\circ}- 40^{\circ}=140^{\circ}\).
Then, divide both sides by 2: \(B_1=\frac{140^{\circ}}{2}=70^{\circ}\).

Answer:

\(70^{\circ}\)