Question

the angles of a triangle are in the ratio 2:3:4 what is the size of its smallest angles ?​

Answer 1

Answer:

40 degrees is the required answer

Answer 2

Given :-

• The angles of a triangle are in the ratio of 2 : 3 : 4.

To Find :-

• What is the smallest angle of a triangle.

Solution :-

Let,

$\mapsto \sf\bold{First\: angle =\: 2x}$

$\mapsto \sf\bold{Second\: angle =\: 3x}$

$\mapsto \sf \bold{Third\: angle =\: 4x}$

As we know that,

$\clubsuit\: \: \sf\boxed{\bold{\pink{Sum\: of\: all\: angle\: in\: triangle =\: 180^{\circ}}}}$

According to the question by using the formula we get,

$\implies \sf 2x + 3x + 4x =\: 180^{\circ}$

$\implies \sf 5x + 4x =\: 180^{\circ}$

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

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

$\implies \sf x =\: \dfrac{20^{\circ}}{1}$

$\implies \sf\bold{\purple{x =\: 20^{\circ}}}$

Hence, the required angle of a triangle are :

$\mapsto$ First angle of a triangle :

$\longrightarrow \sf 2x$

$\longrightarrow \sf 2(20^{\circ})$

$\longrightarrow \sf 2 \times 20^{\circ}$

$\longrightarrow \sf\bold{\red{40^{\circ}}}$

$\mapsto$ Second angle of a triangle :

$\longrightarrow \sf 3x$

$\longrightarrow \sf 3(20^{\circ})$

$\longrightarrow \sf 3 \times 20^{\circ}$

$\longrightarrow \sf\bold{\red{60^{\circ}}}$

$\mapsto$ Third angle of a triangle :

$\longrightarrow \sf 4x$

$\longrightarrow \sf 4(20^{\circ})$

$\longrightarrow \sf 4 \times 20^{\circ}$

$\longrightarrow \sf\bold{\red{80^{\circ}}}$

Hence,

$\bigstar\: \: \sf\bold{\pink{First\: angle =\: 40^{\circ}}}$

$\bigstar\: \: \sf\bold{\pink{Second\: angle =\: 60^{\circ}}}$

$\bigstar\: \: \sf\bold{\pink{Third\: angle =\: 80^{\circ}}}$

$\therefore$ The angle of a triangle is 40°, 60° and 80° respectively.

$\therefore$ The smallest angle of a triangle is 40°.

VERIFICATION :-

$\implies \sf 2x + 3x + 4x =\: 180^{\circ}$

By putting x = 20° we get,

$\implies \sf 2(20^{\circ}) + 3(20^{\circ}) + 4(20^{\circ}) =\: 180^{\circ}$

$\implies \sf 40^{\circ} + 60^{\circ} + 80^{\circ} =\: 180^{\circ}$

$\implies \sf\bold{\green{ 180^{\circ} =\: 180^{\circ}}}$

Hence, Verified.