**Properties of Triangle Worksheet 2 :**

This is the continuity of our web content given on "Properties of Triangle Worksheet 1".

Before we look at the problems, if you want to know the properties of triangle in detail,

**Problem 1 : **

If the angles of a triangle are in the ratio 2 : 7 : 11, then find the angles.

**Problem 2 : **

In a triangle, if the second angle is 10% more than the first angle and the third angle is 20% less than the first angle, then find the three angles of the triangle.

**Problem 3 : **

If 3 consecutive positive integers be the angles of a triangle, then find the three angles of the triangle.

**Problem 4 : **

In a triangle, if the second angle is 2 times the first angle and the third angle is 3 times the first angle, find the angles of the triangle.

**Problem 1 : **

If the angles of a triangle are in the ratio 2 : 7 : 11, then find the angles.

**Solution :**

From the ratio 2 : 7 : 11,

the three angles are 2x, 7x, 11x

In any triangle, sum of the angles = 180°

So, 2x + 7x + 11x = 180°

20x = 180 -------> x = 9

Then, the first angle = 2x = 2(9) = 18°

The second angle = 7x = 7(9) = 63°

The third angle = 11x = 11(9) 99°

Hence the angles of the triangle are (18°, 63°, 99°)

**Problem 2 : **

In a triangle, if the second angle is 10% more than the first angle and the third angle is 20% less than the first angle, then find the three angles of the triangle.

**Solution :**

Let "x" be the first angle.

The second angle = 120 % of x = 1.2x

The third angle = 80% of x = 0.8x

We know that,

the sum of the three angles of a triangle = 180°

x + 1.2x + 0.8x = 180°

3x = 180°

x = 60°

The first angle = 60°

The second angle = 1.2(60) = 72°

The third angle = 0.8(60) = 48°

Hence, the three angles of a triangle are 60°, 72° and 48°.

**Problem 3 : **

If 3 consecutive positive integers be the angles of a triangle, then find the three angles of the triangle.

**Solution :**

Let "x" be the first angle.

The second angle = x + 1

The third angle = x + 1 + 1 = x + 2

We know that,

the sum of the three angles of a triangle = 180°

x + x + 1 + x + 2 = 180°

3x + 3 = 180°

3x = 177°

x = 59°

The first angle = 59°

The second angle = 59 + 1 = 60°

The third angle = 60 + 1 = 61°

Hence, the three angles of a triangle are 59°, 60° and 61°.

**Problem 4 : **

In a triangle, if the second angle is 2 times the first angle and the third angle is 3 times the first angle, find the angles of the triangle.

**Solution :**

Let "x" be the first angle.

The second angle = 2x

The third angle = 3x

We know that,

the sum of the three angles of a triangle = 180°

x + 2x + 3x = 180°

6x = 180°

x = 30°

The first angle = 30°

The second angle = 2(30°) = 60°

The third angle = 3(30°) = 90°

Hence, the three angles of a triangle are 30°, 60° and 90°.

Apart from the problems given above, if you need more problems on triangle properties, please click the following links.

**Worksheet on Properties of Triangle**

**Worksheet on Properties of Triangle 1**

**Worksheet on Properties of Triangle 3**

After having gone through the stuff given above, we hope that the students would have understood the properties of triangle.

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