Question

The angles of a triangle are in the ratio 3:5:10.Find the measures of each angles of the triangle.

Answer 1

Let the angles of the triangle be 3x,5x,10x
Now
3x+5x+10x=180°(since sum of 3 angles of a Δ=180°)
or 18x = 180°
or x =10°
Now angles of the triangle are 3*10°=30°,5*10°=50° and 10*10°=100°

Answer 2

The angles of the triangle are 30° , 50° , 100° respectively

Given :

The angles of a triangle are in the ratio 3 : 5 : 10

To find :

The measures of each angles of the triangle.

Solution :

Step 1 of 2 :

Form the equation to find the angles

Here it is given that the angles of the triangle are in the ratio 3 : 5 : 10

Let the angles of the triangle are 3x , 5x , 10x respectively

We know that , for a triangle sum of three angles = 180°

So by the given condition

3x + 5x + 10x = 180°

Step 2 of 2 :

Find the measures of each angles of the triangle.

3x + 5x + 10x = 180°

⇒ 18x = 180°

⇒ x = 180°/18

⇒ x = 10°

Thus we get ,

1st angle = 3x = 3 × 10° = 30°

2nd angle = 5x = 5 × 10° = 50°

3rd angle = 10x = 10 × 10° = 100°

Hence angles of the triangle are 30° , 50° , 100° respectively

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