Question

the angles of a triangle are in the ratio1:2:3 find their measures in degree

Answer 1

Given :-

Angles of triangle are in the ratio = 1:2:3

To Find :-

Their measures in degree :-

Solution Start :-

Let the 1st angle = 1x

Let the 2nd angle = 2x

Let the 3rd angle = 3x

Angle Sum of the triangle = 180°

1x + 2x + 3x = 180°

6x = 180°

$= > \: \: x = \frac{180}{6}$

$= >x = \: \: \frac{\cancel {180}}{\cancel {6}} = 30$

So the value of x = 30°

Put the value of x = 30 in given angles :-

=> 1st angle = 1(30 ) = 1 × 30 = 30°

=> 2nd angle = 2(30) = 2 × 30 = 60°

=> 3rd angle = 3(30) = 3 × 30 = 90°

Their measures in degree are 30°, 60°, and 90°

Answer 2

To find : measure of angels of triangle .

Given : angles of a triangle are in the ratio $1:2:3$

Solution :  

• As per given data angles of a triangle are in the ratio $1:2:3$  .
• According to angle sum property we know that  sum of measure of all three angles of triangle is $180$ ° .
• Let , $1x , 2x, 3x$ be the angels of triangle .
• Therefore , we have ,

        $1x + 2x + 3x = 180$  

        $6x =180\\x = \frac{180}{6} \\x = 30$

• Now , substituting the value of $x$ in the angles $1x , 2x, 3x$ .  
• $1x =1\times 30 = 30$°

        $2x =2\times 30 = 60$°

        $3x = 3\times 30 = 90$°

Hence , angles of a triangle are in the ratio $1:2:3$  are $30$° ,$60$° ,$90$ ° .