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Two rays that share the same endpoint form an angle. The rays are called the arms of the angle and the common end point is called the vertex.

Types of angles

Angles can be of different types depending on their measure. Let us take a look at the different types of angles.

Zero angle
An angle of measure 0° is called a zero angle.

                                                     
Acute angle
An angle whose measure is more than 0° and less than 90° is called an acute angle.

                                                   
Right angle
An angle whose measure is 90° is called a right angle.

                                                  
Obtuse angle
An angle whose measure is more than 90° and less than 180° is called an obtuse angle.

                                                   
Straight angle
An angle whose measure is 180° is called a straight angle.

                                                   
Reflex angle
An angle whose measure is more than 180° and less than 360° is called a reflex angle.

                                                    
Complete angle
An angle whose measure is 360° is called a complete angle.

                                                     

Related terms
Let us take a look at some other terms related to angles that are commonly used in geometry.

Complementary angles
A pair of angles are called complementary to each other,if the sum of their measures is 90°.

Supplementary angles
A pair of angles are called supplementary to each other, if the sum of their measures is 180°.

Adjacent angles
Two angles are called adjacent if they have the same vertex, a common arm and the other arms of the two angles are on the opposite sides of the common arm.

Vertically opposite angles
If two straight lines intersect at a point, vertically opposite angles are formed. The measures of vertically opposite angles are equal.

Practice questions:

Question: Draw the following angles with the correct measures and identify the type of angle
1. Angle AOB measuring 60°
2. Angle CED measuring 90°
3. Angle BOC measuring 135°
4. Angle DEF measuring 180°
5. Angle FOG measuring 270°
6. Angle LOP measuring 360°

Question: Write the measures of the complementary and supplementary angles of the following angles (Remember complementary angles should add up to 90° and supplementary angles should add up to 180°) :

Angle

Complementary

Supplementary

 65°

   

 37°

   

 80°

   

 14°

   

 20°

   
 65°    

 

Question: Calculate the value of x in the following

                                                         

( Answer:
    Angle AOC = 90° ( Right angled triangle)
    Angle AOB + Angle BOC = 90° (Sum of all the angles in a Right angled triangle is 90°)
    X + 55° = 90°
    X = 90° - 55° = 35°
    
    Angle BOC = 35°
)

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