Question

Question 8
Show that the angles of an equilateral triangle are ${60}^{\circ }$ each

Answer 1

$\Delta ABCisequilateralwhichmeansthatAB=BC=AC.AB=BC\Rightarrow \angle B=\angle C(Intriangle,anglesoppositetoequalsidesareequal)...\left(1\right)AB=BC\Rightarrow \angle A=\angle C(Intriangle,anglesoppositetoequalsidesareequal)...\left(2\right)From\left(1\right)and\left(2\right),wecansaythat\angle A=\angle B=\angle C...\left(3\right)Also,\angle A+\angle B+\angle C={180}^{\circ }\left(Anglesumpropertyoftriangle\right)Putting\left(3\right)intheaboveequation,weget\angle A+\angle A+\angle A={180}^{\circ }\Rightarrow 3\angle A={180}^{\circ }\Rightarrow \angle A=\frac{180}{3}={60}^{\circ }...\left(4\right)From\left(3\right)and\left(4\right),wecansaythat\angle A=\angle B=\angle C={60}^{\circ }$