Question

Show that the angle of an equilateral triangle are 60° each.

Answer 1

Assumption

${\boxed{\sf\:{PQR\;be\;an\;Equilateral\;Triangle }}}$

PQ = QR = PR

Hence we have,

PQ = PR

So,

${\boxed{\sf\:{\angle Q=\angle R.....(1)}}}$

Also we have

PQ = QR

${\boxed{\sf\:{\angle P=\angle R.......(2)}}}$

As from Equation (1) and (2) we have,

∠P = ∠Q = ∠R ....... (3)

Also now

∠P + ∠Q + ∠R = 180 (Sum of angle of Triangle)

From (3) we have,

${\boxed{\sf\:{\angle P =\angle P =\angle P = 180}}}$

3∠P = 180

$\tt{\rightarrow \angle P=\dfrac{180}{3}}$

∠P = 60

Therefore

From (3) we get,

∠P = ∠Q = ∠R = 60