Question

In a $△ABC,\angle A=x^{\circ },\angle B=(3x-2{)}^{\circ },\angle C=y^{\circ }$. If 3y – 5x = 30. Prove that the triangle is right angled.

Answer 1

Sum of angles of triangle = 180

A+B+C=180
$x+3x-2+y=180$
$4x+y=182$ ---(i)

$3y-5x=30$ ---- (ii)

5(i) + 4(ii)

$20x+5y=910$
$-20x+12y=120$
-------------------
$17y=1030$

$y=1030/17$

$4x=182-\frac{1030}{17}$

$x=\frac{516}{17}=30.35$

$3x-2=89.05$

Hence the triangle is not a right-angled triangle