Question

an isosceles triangle is a triangle in which two sides are equal in length. the angle between the two equal sides is called the vertex angle, while the other two angles are called the base angles. if the vertex angle is 80°, what is the measure of the base angles?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let the measure of each base angle be $x$.

Step2: Set up an equation

We know that the vertex angle is $80^{\circ}$ and there are two base angles of measure $x$ each. So, $80 + 2x=180$.

Step3: Solve the equation for $x$

First, subtract 80 from both sides of the equation: $2x=180 - 80$. So, $2x = 100$. Then divide both sides by 2: $x=\frac{100}{2}=50$.

Answer:

$50^{\circ}$