Question

The angles of the triangle are in the ratio 5:3:10 .. Then find the angles??​

Answer 1

Given :

• The angles of the triangle are in the ratio = 5:3:10.

To Find :

• The required angles .

Solution :-

We know that ,

$\bigstar{ \boxed{\tt{ \red{Sum\: of \: all \: angles \: of \: triangle = 180^ {\circ}}}}}\bigstar$

Let

• First angle = (5x)°.
• Second angle = (3x)°
• Third angle = (10x)°.

According to the question,

$: \implies{ \sf{5x + 3x + 10x = 180}}$

$: \implies {\sf{18x = 180}}$

$: \implies {\sf{x = \cancel{ \dfrac{180}{18}}}}$

$: \implies { \boxed{\tt{x = 10}}}$

$\therefore{\underline{\sf{ \pink{First \: angle = {(5 \times 10)} ^{ \circ} = 50^{ \circ}.}}} }$

$\therefore{ \underline{\sf{ \pink{Second \: angle = {(3\times 10)} ^{ \circ} = 30^{ \circ}.}}}}$

$\therefore{ \underline{\sf{ \pink{Third\: angle = {(10\times 10)} ^{ \circ} = 100^{ \circ}.}}}}$

Verification :

We have,

• First angle = 50°
• Second angle = 30°
• Third angle = 100°

$: \implies{ \sf{50^ {\circ}+ 30^ {\circ}+ 100^ {\circ}= 180^ {\circ}}}$

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

$: \implies { \boxed{\tt{LHS= RHS}}}$

$\therefore{\underline{\bf{Verified.}}}$

Answer 2

Given :

The angles of the triangle are in the ratio = 5:3:10.

To Find :

The required angles .

Solution :-

We know that ,

$\bigstar{ \boxed{\tt{ \red{Sum\: of \: all \: angles \: of \: triangle = 180^ {\circ}}}}}\bigstar$

Let

First angle = (5x)°.

Second angle = (3x)°

Third angle = (10x)°.

According to the question,

$: \implies{ \sf{5x + 3x + 10x = 180}}$

$: \implies {\sf{18x = 180}}$

$: \implies {\sf{x = \cancel{ \dfrac{180}{18}}}}$

$: \implies { \boxed{\tt{x = 10}}}$

$\therefore{\underline{\sf{ \pink{First \: angle = {(5 \times 10)} ^{ \circ} = 50^{ \circ}.}}} }$

$\therefore{ \underline{\sf{ \pink{Second \: angle = {(3\times 10)} ^{ \circ} = 30^{ \circ}.}}}}$

$\therefore{ \underline{\sf{ \pink{Third\: angle = {(10\times 10)} ^{ \circ} = 100^{ \circ}.}}}}$

Verification :

We have,

First angle = 50°

Second angle = 30°

Third angle = 100°

$: \implies{ \sf{50^ {\circ}+ 30^ {\circ}+ 100^ {\circ}= 180^ {\circ}}}$

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

$: \implies { \boxed{\tt{LHS= RHS}}}$

$\therefore{\underline{\bf{Verified.}}}$✅