Question

Find all the angles of an equilateral triangle.

Answer 1

Find the angles of an equilateral triangle.

According to the theorem, angles opposite to equal sides are equal.

We know that, in an equilateral triangle, all the sides are equal.

Thus, all the angles are also equal.

Let the angles of an equilateral triangle be $x°$.

According to the Angle Sum Property, the sum of all the interior angles of a triangle is equal to $180°$.

$$\begin{gathered} \Rightarrow x°+x°+x°=180° \\ \Rightarrow 3x°=180° \\ \Rightarrow x°=\frac{180°}{3} \\ \Rightarrow x°=60° \end{gathered}$$

Therefore, all the angles of an equilateral triangle are $60°$.