# Ex.7.2 Q8 Triangles Solution - NCERT Maths Class 9

## Question

Show that the angles of an equilateral triangle are \(60^{\circ}\) each.

## Text Solution

**What is Known?**

Triangle \(ABC\) is an equilateral triangle.

**To prove:**

The angles of an equilateral triangle are \(60º\) each.

**Reasoning:**

We can use the property angles opposite to equal sides are equal and then by the angle sum property in triangle \(ABC\) we can show the value of each angle is \(60\) degree.

**Steps:**

Let us consider that \(ABC\) is an equilateral triangle.

Therefore,

\[\begin{align} &AB=BC=AC \\ &AB=AC \\ \therefore \,&\angle C=\angle B \\ & \left( \begin{array}{I} \text{Angles opposite to equal sides } \\ \text{of a triangle are also equal}\text{.} \\

\end{array} \right) \\ \end{align}\]

Therefore, we obtain \(\angle A = \angle B = \angle C\)

In \(\Delta ABC,\)

\[\begin{align} \angle A+\angle B+\angle C&=180^{\circ} \\ \angle A+\angle A+\angle A&=180^{\circ} \\ 3\angle A&=180^{\circ} \\ \angle A&=60^{\circ} \\ \therefore \angle A=\angle B&=\angle C=60^{\circ} \\ \end{align}\]

Hence, in an equilateral triangle, all interior angles are of measure \(60^{\circ}\).