Question

in triangle if angle A=3x angle B=6x and angle C=x findthe measures of the angle

Answer 1

Answer:

Given :-

• In a triangle ABC, ∠A = 3x, ∠B = 6x and ∠C = x.

To Find :-

• What is the measure of the angle of triangle.

Solution :-

Given :

$\mapsto \bf \angle{A} =\: 3x$

$\mapsto \bf \angle{B} =\: 6x$

$\mapsto \bf \angle{C} =\: x$

As we know that :

$\footnotesize \bigstar\: \: \sf\boxed{\bold{\pink{Sum\: of\: all\: three\: angles_{(Triangle)} =\: 180^{\circ}}}}\: \: \bigstar$

According to the question by using the formula we get,

$\implies \sf\bold{\green{\angle{A} + \angle{B} + \angle{C} =\: 180^{\circ}}}$

$\implies \sf 3x + 6x + x =\: 180^{\circ}$

$\implies \sf 9x + x =\: 180^{\circ}$

$\implies \sf 10x =\: 180^{\circ}$

$\implies \sf x =\: \dfrac{\cancel{180^{\circ}}}{\cancel{10}}$

$\implies \sf\bold{\purple{x =\: 18^{\circ}}}$

Hence, the required angles of triangle :

$\clubsuit \: \: \bf \angle{A} =\: 3x$

$\dashrightarrow \sf \angle{A} =\: 3(18^{\circ})$

$\dashrightarrow \sf\bold{\red{\angle{A} =\: 54^{\circ}}}$

$\clubsuit \: \: \bf \angle{B} =\: 6x$

$\leadsto \sf \angle{B} =\: 6(18^{\circ})$

$\leadsto \sf\bold{\red{\angle{B} =\: 108^{\circ}}}$

$\clubsuit \: \: \bf \angle{C} =\: x$

$\mapsto \sf\bold{\red{\angle{C} =\: 18^{\circ}}}$

$\therefore$ The measure of the angle of triangle are 54°, 108° and 18° respectively.

Answer 2

Answer:

• Refer the attachment for steps :)