Here we will prove that the three angles of an equilateral triangle are equal.

**Given:** PQR is an equilateral triangle.

**To prove:** ∠QPR = ∠PQR = ∠ PRQ.

**Proof:**

1. ∠QPR = ∠PQR 2. ∠PQR = ∠ PRQ. 3. ∠QPR = ∠PQR = ∠ PRQ. (Proved). |
1. Angles opposite to equal sides QR and PR. 2. Angles opposite to equal sides PR and PQ. 3. From statement 1 and 2. |

**Note:**

**1.** In the equilateral ∆PQR, let ∠PQR = ∠PRQ = ∠RPQ = x°. Therefore, 3x° = 180° as
the sum of the three angles of a triangle is 180°.

Therefore, x° = \(\frac{180°}{3}\)

⟹ x° = 60°.

Thus, each angle of an equilateral triangle is 60°.

**2.** If one angle of an
isosceles triangle is given, the other two can be easily found out.

In the given figure, PQ = PR.

Therefore, ∠PQR = ∠PRQ = x° (suppose).

Let ∠RPQ = y°

Thus, y° + 2x° = 180°, from which we get

y° = 180° - 2x°

and x° = \(\frac{180° - y°}{2}\).

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