Question

the angles of a triangles are in ratio of 1 2 3 find the angles

Answer 1

To find : angles of triangle .

Given ratio of angles : $1 : 2 :3$

Solution :

• Let , three angles of triangle of be $1x , 2x, 3x$ .

• Then according to angle sum property of triangle sum of all three angles of triangle is $180$° .
• Therefore , according to angle sum property we have ,

        $1x + 2x+ 3x = 180 \\6x =180\\x = 30$

• Angles of triangle  are : $1x = 1\times 30 =30$°

                                                $2x = 2\times 30 =60$°

                                                $3x = 3\times 30 =90$°

Hence , angles of triangle are  $30$° ,$60$° ,$90$°  .

Answer 2

Step-by-step explanation:

Given :

• The angles of a triangle are in the ratio 1 : 2 : 3.

To Find :

• The angles.

Solution :

Let the common ratio x.

✴️ Let's assume that,

• 1st angle = x
• 2nd angle = 2x
• 3rd angle = 3x

We know that,

★ Sum of all the angles of a triangle is 180°.

$\\ \sf \longrightarrow \: x + 2x + 3x = {180}^{ \circ} \\ \\ \sf \longrightarrow \: 3x + 3x = {180}^{ \circ} \\ \\ \sf \longrightarrow \: 6x= {180}^{ \circ} \\ \\ \sf \longrightarrow \: x = \dfrac{180}{6} \\ \\ \sf \longrightarrow \: x = \dfrac{ \cancel{180}}{ \not6} \\ \\ \red{\sf \longrightarrow \: \boxed{\bf x = {30}^{ \circ} } \: \bigstar}$

~Now, finding angles :

★ 1st angle :

$\longrightarrow$ x°

$\longrightarrow$ 30°

★ 2nd angle :

$\longrightarrow$ 2x°

$\longrightarrow$ 2(30)°

$\longrightarrow$ 60°

★ 3rd angle :

$\longrightarrow$ 3x°

$\longrightarrow$ 3(30)°

$\longrightarrow$ 90°

Hence, the angles of a triangle are 30°, 60° and 90°.