**Determining angle visually : **

Here we are going to see, how to determine the type of the angle visually.

In geometry, angles can be classified according to the size.

There are five different types of angles.

The following table explains "How angles in geometry can be determined visually"

**Type of Angle**

**Description**

**Determining angle visually **

Acute angle

An angle that is less than 90°

Right angle

An angle that is exactly 90°

Obtuse angle

An angle that is greater than 90° but less than 180°

Straight angle

An angle that is exactly 180°

Reflex angle

An angle that is greater than 180° but less than 360°

Full angle

An angle that is exactly 360°

**Problem 1 :**

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that the angles "x" and "2x" together form a right angle.

So, we have x + 2x = 90°

3x = 90°

x = 30°

**Hence the value of "x" is 30°.**

Let us look at the next problem on "Determining angle visually"

**Problem 2 :**

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that the angles (x+1), (x-1) and (x+3) together form a right angle.

So, we have (x+1) + (x-1) + (x+3) = 90

3x + 3 = 90

3x = 87

x = 29

**Hence the value of "x" is 29.**

Let us look at the next problem on "Determining angle visually"

**Problem 3 :**

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that the angles (2x+3) and (x-6) together form a straight angle.

So, we have (2x+3) + (x-6) = 180°

2x + 3 + x - 6 = 180°

3x - 3 = 180

3x = 183

x = 61

**Hence the value of "x" is 61.**

**Let us look at the next problem on "Determining angle visually"**

**Problem 4 :**

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that the angles (5x+4), (x-2) and (3x+7) together form a straight angle.

So, we have (5x+4) + (x-2) + (3x+7) = 180°

5x + 4 + x -2 + 3x + 7 = 180°

9x + 9 = 180

9x = 171

x = 19

**Hence the value of "x" is 19.**

**Let us look at the next problem on "Determining angle visually"**

**Problem 5 : **

If 4 times the sum of an angle and 5 is 32, find the type of the angle.

**Solution :**

Let "x" be the required angle.

According to the question, we have

4(x + 5) = 32

4x + 20 = 32

4x = 12

x = 3

Angle = 3°

**Since the angle 3° is less than 90°, the type of the angle is acute angle. **

**Let us look at the next problem on "Determining angle visually"**

**Problem 6 : **

If 2 times the sum of 3 times of an angle and 20 is 1024, find the type of the angle.

**Solution :**

Let "x" be the required angle.

According to the question, we have

2(3x + 20) = 1024

3x + 20 = 512

3x = 498

x = 166

Angle = 166°

**Since the angle 166° is greater than 90° but less than 180****°, the type of the angle is obtuse**** angle.**

**Problem 7 : **

If the sum of 5 times of an angle and 2 is 1222, find the type of the angle.

**Solution :**

Let "x" be the required angle.

According to the question, we have

5x + 2 = 1222

5x = 1220

x = 244

Angle = 244°

**Since the angle 244° is greater than 180° but less than 360****°, the type of the angle is reflex**** angle. **

**Problem 8 : **

If the sum of 5 times of an angle and 2 is 1222, find the type of the angle.

**Solution :**

Let "x" be the required angle.

According to the question, we have

5(x - 2) = 440

x - 2 = 88

x = 90

Angle = 90°

**Since the angle is exactly 90°****, the type of the angle is right angle****.**

**Problem 9 : **

If 7 times the difference between 3 times of an angle and 5 is 3745, find the type of the angle.

**Solution :**

Let "x" be the required angle.

According to the question, we have

7(3x - 5) = 3745

3x - 5 = 535

3x = 540

x = 180

Angle = 180°

**Since the angle is exactly 180°****, the type of the angle is straight angle****. **

**Problem 10 : **

If 2 times the difference between 9 times of angle and 15 is 6450, find the type of the angle.

**Solution :**

Let "x" be the required angle.

According to the question, we have

2(9x - 15) = 6450

9x - 15 = 3225

9x = 3240

x = 360

Angle = 360°

**Since the angle is exactly 360°****, the type of the angle is full angle****. **

**Classify the angles as acute, right, obtuse straight, reflex or full angle : **

1) 35° ---> Acute angle

2) 85° ---> Acute angle

3) 95° ---> Obtuse angle

4) 135° ---> Obtuse angle

5) 205° ---> Reflex angle

6) 180° ---> Straight angle

7) 90° ---> Right angle

8) 360° ---> Full angle

9) 15° ---> Acute angle

10) 270° ---> Reflex angle

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