Question

Hello,-4, U and 4 on number line.
5. The ratio of angles of a triangle is 1:2:3. Find the angles and name the triangle​

Answer 1

Answer:-

⠀⠀⠀⠀⠀⠀⠀⠀⠀According to the Question

Let the ratio of angle of triangle be x : 2x : 3x

As we know that sum of all angles in triangle is 180°

Substitute the value we get

$:\implies$ x + 2x + 3x = 180°

$:\implies$ 3x+3x = 180°

$:\implies$ 6x = 180°

$:\implies$ x = 180°/6

$:\implies$ x = 30°

So the value of x = 30°

Now , putting the value

$:\implies$ x = 30°

$:\implies$ 2x = 2×30 = 60°

$:\implies$ 3x = 3×30° = 90°

• Hence, the angles of the triangle is 30° , 60° & 90° respectively.

Since , one angle is 90°

So ,the triangle is Right Angle Triangle .

Answer 2

Question:-

• The ratio of angles of a triangle is 1:2:3. Find the angles and name the triangle.

To Find:-

• Find the angles and name the triangle.

Solution:-

• Let the first angle be x

• Second angle be 2x

• Third angle be 3x

According to the Question:-

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

$\dashrightarrow\sf \: 6x = {180}^{\circ}$

$\dashrightarrow\sf \: x = \cancel\dfrac { 180 } { 6 }$

$\dashrightarrow\sf \: x = 30$

Now ,

We have to find the angles by substituting ‘ x ’ value:-

$\dashrightarrow\sf \: First \: angle = {30}^{\circ}$

$\dashrightarrow\sf \: Second\: angle = 2( 30 ) → { 60 }^{\circ }$

$\dashrightarrow\sf \: Third \: angle = 3( 30 ) → { 90 }^{\circ }$

Hence ,

• The triangle is right angled.