Question

(b)
If angles of a triangle are in the ratio 1:2:3. find the value of each angle. ​

Answer 1

Let the number be X

So

1x +2x +3x = 180

6x =180

X =30

1x =30 degree

2x =60 degree

3x =90 degree

Answer 2

Answer :-

• The angles are 30°, 60° and 90°.

Given :-

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

To find :-

• The value of each angle.

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Step-by-step explanation :-

We know that the angles of a triangle are in the ratio 1 : 2 : 3. We have to find the value of each angle.

Since they are in the ratio 1 : 2 : 3,

Therefore let the angles be x, 2x and 3x.

We know that :-

Sum of all the angles in a triangle = 180°.

So, clearly, all these angles will add up to 180°.

Therefore, we get :-

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

Adding all the variables,

$\sf6x = 180^{\circ}$

Transposing 6 from LHS to RHS, changing it's sign,

$\sf x = \dfrac{180^{\circ}}{6}$

Dividing 180 by 6,

$\sf x = 30^{\circ}.$

Since x = 30°.

Therefore, the angles of the triangle are as follows :-

$\sf x = 1 \times 30^{\circ} = 30^{\circ}.$

$\sf2x = 2 \times 30^{\circ} = 60^{\circ}.$

$\sf3x = 3 \times 30^{\circ} = 90^{\circ}$

So, the value of the angles of the triangle are 30°, 60° and 90°.