Question

1.) The angles of a triangle are in the ratio 2:4:6 .Find the angles of the triangle .
2.) Two angles of a triangle are 70° and 30° .Find the 3rd angle .​

Answer 1

1 ) To find : angles of triangle .

Given : The angles of a triangle are in the ratio $2 : 4: 6$ .

Solution :

• Let , $2x , 4x ,6x$ be the angles of triangle.
• We know that according to angle sum property of triangle , sum of all the angles of triangle $180$° .

• Therefore , we have ,  $2x + 4x + 6x =$ $180$°  

                                                             $12x=$ $180$°  

                                                                 $x = 15$

• Hence , $2x = 2 \times 15 =$ $30$°

                     $4x = 4\times 15 =$$60$°

                     $6x = 6\times 15 =$ $90$°

Hence , three angles are $30$°,$60$° ,$90$° .

2 )To find : Third angle of triangle .

   Given :  Two angles of a triangle are $70$° and $30$° .

  Solution :  

• Let missing angle be $x$ .
• Then , $70 + 30 + x =$ $180$°  

                                   $x =$ $180$°  $- 100$°

                                   $x = 80$°

Hence , third angle is $80$° .

Answer 2

Answer 1

Given :

Ratio of the angles of the triangle = 2 : 4 : 6

To find :

The all angles

Solution :

Let the angles be - 2x , 4x and 6x

By angle sum property

$\implies \tt2x + 4x + 6x = 180 \\ \implies \tt12x = 180 \\ \tt \implies \tt x = \frac{180}{12} \\ \implies \tt \: x = 15$

$\tt \: Now, \: Value \: of \: 2x \\ \tt\implies 2(15) \\ \tt \implies 30° \\ \\ \tt \: Value \: of \: 4x \\ \tt\implies 4(15) \\ \tt\implies 60° \\ \\ \tt \: Value \: of \: 6x \\ \tt \implies \: 6(15) \\ \tt\implies 90$

$\boxed{ \tt \red{\therefore \: The \: angles \: of \: the \: triangle \: are \: 30°, \: 60° \: and \: 90°.}}$

Answer 2

Given

Two angles of the triangle are 70° and 30°

To find

The third angle

Solution

Let the third angle be x

$\bf{70\degree+30\degree+X=180} \\ \bf{100 \degree+X=180 \degree} \\ \bf{X=180 \degree-100 \degree} \\\bf{X=180 \degree}$$\boxed{ \bf \red{ \therefore the \: third \: angle \: is \: 180 \degree}}$