Question

in a triangle ABC angle A is = x degree angle b is = 3 X degree and Angle C is = Y degree. if 3 Y - 5 x is = 30. prove that the triangles is right angled.





please give me answer.........

Answer 1

Answer is in link.
# triangle ABC here is not expressed as right angled since we don't know whether it is right angled or not.....

Answer 2

$\large{\color{blue}{\bf HELLO \: \: DEAR,}}$

$\bf given \: \: that:- < A = x , < B = 3x , < C = y \\ \\ \bf 3y - 5x = 30 \\ \\ \bf3y = 30 + 5x----------( 1 ) \\ \\ \bf we \:\:know \:\:that:- \\ \\ \bf sum \:\: of \:\: angle\:\: of \:\: \triangle = 180 \degree \\ \\ \bf x + 3x + y = 180\degree \\ \\ \bf 12x + 3y = 540\degree \\ \\ \bf 12x + 5x + 30 = 540\degree \\ \\ \bf 17x = 510\degree \\ \\ \bf x = 30\degree [ put\:\: in ----( 1 )] \\ \\ \bf we\:\: get, \\ \\ \bf 3y = 5x + 30 \\ \\ \bf 3y = 5(30) + 30 \\ \\ \bf 3y = 180\degree \\ \\ \bf y = 60\degree , x = 30\degree \\ \\ \bf < A = 30\degree , < B = 3(30) = 90\degree , < C = 60\degree$

$\bf \: we \: \: know \: \: in \: \: right \: \: angle \: \: \triangle \: \: its \: \: one \: \: angle \: \: is \: \: 90\degree \\ \\ \\ \bf \: hence, \: \: it \: \: is \: \: right \: \: angle \: \: \triangle$

$\color{red} \bf \underline{\bf I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}$