**Types of Angles : **

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

There are six different types of angles.

Let us see, how how angles in geometry can be classified.

**Type of Angle**

**Description**

**Example**

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°

**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

**Problem 1 : **

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.

**Problem 2 : **

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 3 : **

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 4 : **

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 5 : **

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 6 : **

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.

After having gone through the stuff given above, we hope that the students would have understood "Types of angles".

If you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Time and work word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**