**Properties of Triangle Worksheet 3 :**

This is the continuity of our web content given on "Properties of Triangle worksheet 2".

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

**Problem 1 : **

In a right triangle, apart from the right angle, the other two angles are x+1 and 2x+5. find the angles of the triangle.

**Problem 2 : **

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

**Problem 3 : **

In a triangle, the ratio between the first and second angle is 1 : 2 and the third angle is 72. Find the first and second angle of the triangle. ** **

**Problem 1 : **

In a right triangle, apart from the right angle, the other two angles are x+1 and 2x+5. find the angles of the triangle.

**Solution :**

We know that,

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

90 + (x + 1) + (2x + 5) = 180°

3x + 6 = 90°

3x = 84°

x = 28°

So,

x + 1 = 28 + 1 = 29°

2x + 5 = 2(28) + 5 = 56 + 5 = 61°

Hence, the three angles of a triangle are 90°, 29° and 61°.

**Problem 2 : **

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

**Solution :**

Let "x" be the first angle.

The second angle = 3(x+3)

The third angle = 2x + 3

We know that,

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

x + 3(x+3) + 2x + 3 = 180°

x + 3x + 9 + 2x + 3 = 180°

6x + 12 = 180°

6x = 168°

x = 28°

The first angle = 28°

The second angle = 3(28+3) = 93°

The third angle = 2(28) + 3 = 59°

Hence, the three angles of a triangle are 28°, 93° and 59°.

**Problem 3 : **

In a triangle, the ratio between the first and second angle is 1 : 2 and the third angle is 72. Find the first and second angle of the triangle. ** **

**Solution :**

From the given ratio,

The first angle = x

The second angle = 2x

We know that,

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

x + 2x + 72 = 180°

3x = 108°

x = 36°

The first angle = 36°

The second angle = 2(36°) = 72°

Hence, the first angle is 36° and the second angle is 72°.

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 2**

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