Question

Find if $\Delta ABC$ is equilateral when:
$\angle A=x+{42}^{\circ },\angle B=4x-{12}^{\circ }$ and $\angle C=3x-6^{\circ }$.

Answer 1

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

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

Given : $\angle A=x+42=60$

$x={18}^o--------\left(1\right)$

$\angle B=4x-12=60$

$4x=72$

$x={18}^o---------\left(2\right)$

$\angle C=3x-6=60$

$3x=66$

$x=22---------\left(3\right)$

From eq $\left(1\right),\left(2\right),\left(3\right)x\ne 18$

Therefore $△ABC$ is not equilateral.