**Worksheet on Types of Triangles :**

Worksheet given in this section is much useful to the students who would like to practice problems on different types of triangles.

Before look at the worksheet, if you would like to know the stuff on different types of triangles,

**Problem 1 :**

Identify the type of triangle whose angles are 35°, 40°, 105°.

**Problem 2 :**

Identify the type of triangle whose angles are 55°, 65°, 60°.

**Problem 3 :**

Identify the type of triangle whose angles are 50°, 40°, 90°.

**Problem 4 :**

Identify the type of triangle whose angles are 45°, 45°, 90°.

**Problem 5 :**

Identify the type of triangle whose angles are 70°, 70°, 40°.

**Problem 6 :**

Identify the type of triangle whose angles are 30°, 30°, 120°.

**Problem 7 :**

Identify the type of triangle whose sides are 5 cm, 6 cm and 7 cm.

**Problem 8 :**

Identify the type of triangle whose sides are 6 cm, 6 cm and 8 cm.

**Problem 9 :**

If (3x + 3) is one of the angles of an acute triangle, then find the value of "x".

**Problem 10:**

If 50°, 40° and (2x + 4)°are the angles of a right triangle, then find the value of "x".

**Problem 1 :**

Identify the type of triangle whose angles are 35°, 40°, 105°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) All the given three angles are different.

(ii) One of the angles is greater than 90°

From the above two points,

The given triangle is a scalene and obtuse triangle.

**Problem 2 :**

Identify the type of triangle whose angles are 55°, 65°, 60°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) All the given three angles are different.

(ii) All the three angles are less than 90°

From the above two points, we have

The given triangle is a scalene and acute triangle.

**Problem 3 :**

Identify the type of triangle whose angles are 50°, 40°, 90°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) All the given three angles are different.

(ii) One of the angles is 90°

From the above two points, we have

The given triangle is a scalene and right triangle.

**Problem 4 :**

Identify the type of triangle whose angles are 45°, 45°, 90°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) Two of the given angles are equal

(ii) One of the angles is 90°

From the above two points, we have

The given triangle is an isosceles and right triangle.

**Problem 5 :**

Identify the type of triangle whose angles are 70°, 70°, 40°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) Two of the given angles are equal

(ii) All the three angles are less than 90°

From the above two points, we have

The given triangle is an isosceles and acute triangle.

**Problem 6 :**

Identify the type of triangle whose angles are 30°, 30°, 120°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) Two of the given angles are equal

(ii) One of the angles is greater than 90°

From the above two points, we have

The given triangle is an isosceles and obtuse triangle.

**Problem 7 :**

Identify the type of triangle whose sides are 5 cm, 6 cm and 7 cm.

**Solution :**

The length of all the three sides are different.

From the above point, we have

The given triangle is a scalene triangle.

**Problem 8 :**

Identify the type of triangle whose sides are 6 cm, 6 cm and 8 cm.

**Solution :**

The lengths of two of the sides are equal.

From the above point, we have

The given triangle is an isosceles triangle.

**Problem 9 :**

If (3x + 3) is one of the angles of an acute triangle, then find the value of "x".

**Solution :**

Since the given triangle is acute triangle, all the three angles will be less than 90°.

So, (3x + 3) will also be less than 90°.

Then,

3x + 3 < 90°

3x < 87°

x < 29°

Hence, the value of "x" is less than 29°.

**Problem 10:**

If 50°, 40° and (2x + 4)°are the angles of a right triangle, then find the value of "x".

**Solution:**

Since the given triangle is a right triangle, one of the angles must be 90°

In the given three angles 50°, 40° and (2x+4)°, the first two angles are not right angles.

So the third angle (2x+4)° must be right angle.

Then,

2x + 4 = 90°

2x = 86°

x = 43°

Hence, the value of "x" is 43°.

After having gone through the stuff given above, we hope that the students would have understood "Worksheet on types of triangles".

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