Question

Show that $\Delta ABC$ is equilateral if
(i)$\angle A=x+{30}^{\circ },\angle B=3x-{30}^{\circ }$ and $\angle C=4x-{60}^{\circ }$

Answer 1

To show: $△ABC$ is equilateral Property of equilateral triangle

$\angle A=\angle B=\angle C=60$

Given : $\angle A=x+30=60$

$x=30-----\left(1\right)$

$\angle B=3x-30=60$

$3x=90$

$x=30-------\left(2\right)$

$\angle C=x-60=60$

$4x=120$

$x=30---------\left(3\right)$

From eq $\left(1\right),\left(2\right),\left(3\right)x=30$

and $\angle A=\angle B=\angle C=60$

Hence , $△ABC=$ equilateral