Question

1. a triangle is equilateral. find the measure of each of its angles.

Explanation:

Step1: Recall the property of an equilateral triangle

An equilateral triangle has all sides equal and all angles equal.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let each angle of the equilateral triangle be \(x\). Then \(x + x+x=180^{\circ}\), which simplifies to \(3x = 180^{\circ}\).

Step3: Solve for \(x\)

Divide both sides of the equation \(3x=180^{\circ}\) by \(3\). So, \(x=\frac{180^{\circ}}{3}=60^{\circ}\).

Answer:

Each angle of the equilateral triangle measures \(60^{\circ}\).