ANGLES

Types of Angles and Lines
 

1. angle1.jpg (10152 bytes) A right angle is an angle of 90° . It is ¼ of a complete turn.
2. angle2.jpg (9062 bytes) This as an acute angle. It is a smaller than a right angle.
3. angle3.jpg (9325 bytes) This angle on a straight line is made up of 2 right angles. It is an angle of 180° which is half of a complete turn.
4. angle4.jpg (11967 bytes) This is an obtuse angle. It is greater than a right angle but smaller than 2 right angle.
5. angle5.jpg (12608 bytes) This angle is made up of 3 right angles. It is an angle of 270° which is ¾ of a complete turn.
6. angle6.jpg (11034 bytes) A reflex angle is an angle which is more than 180° but less than 360° .
7.   angle7.jpg (7806 bytes) This angle is made up of 4 right angles. It is an angle of 360° which is 1 complete turn.
8. angle8.jpg (13774 bytes) Angles x, y and z are adjacent angles on a straight line. Adjacent angles on a straight line add up to 180°.
9. angle9.jpg (24000 bytes) / a, / b, / c and / d are angles at a point. Angles at a point add up to 360° or 4 right angles.
10. angle10.jpg (17119 bytes) / a = / b

/ y = / z

Vertical opposite angles

Vertically opposite angles are formed where two straight lines cut one another. They are equal.
11. angle11.jpg (16111 bytes) AB and CD are a pair of perpendicular lines. Two straight lines are perpendicular if they meet at right angles.
12. angle12.jpg (26874 bytes) WX is parallel to YZ (WX // YZ). AB, CD and EF are parallel lines. Two or more lines are parallel if they never meet when they are produced.
13. angle13.jpg (27718 bytes) AB is parallel to CD (AB // CD)

/ w = / x

/ y = / z

Corresponding angles

Corresponding angles are equal.
14. angle14.jpg (25616 bytes) AB is parallel ot CD 

/ w = / x

/ y = / z

Alternative angles

Alternative angles are equal.
15. angle15.jpg (22519 bytes) / w = / x = 180°

/ y = / z = 180°

Interior angles

Interior angles add up to 180° . 


 
 
 

Types of Triangles
 

1. angle16.jpg (21920 bytes) ABC is a right-angled triangle.

/ ABC is a right angle (90° ) and AB is perpendicular to BC.

The sum of the three angles in a triangle is equal to 2 right angles or 180° .

/ a + / b+ / c = 180° .
2. angle17.jpg (18789 bytes) ABC is an equilateral triangle. 
All the angles are equal. / a = / b = / c = 60° .

All the sides are equal. AB = BC = CA.
3. angle18.jpg (22783 bytes) ABC is an isosceles triangle. The base angles are equal. / a = / b

The two sides are equal. AB = AC.
4. angle19.jpg (21092 bytes)

 

 The exterior angle of a triangle is equal to the sum of two interior opposite angles.

/ z = / x + / y

Examples:

  1. Find the value of x in the figure below.

    angle20.jpg (23994 bytes)

    x + 60° + 2x + x = 180° ( Adjacent angles on a straight line )

    4x = 180° - 60° 
    = 120° 

    x = 120° 
             4 
    = 30° 
     
     

  2. Find the value of x.

    angle21.jpg (24388 bytes)

    58° + 90° + 125° + x = 360° ( Angles at a point )
    x = 360° - (58° + 90° + 125° )
    = 360° - 273° 
    = 87° 
     
  3. Find / a in the figure.

    angle22.jpg (22244 bytes)
     
     
    130° + / b = 180° ( Adjacent angles on a straight line )
    / b = 180° - 130° 
    = 50° 
    / a = 58° + 50° (Exterior angle = sum of 2 interior opposite angles )
    = 108° 

  4. In the figure AG = AF and BD// GE. Calculate / a and / b.
     
      angle23.jpg (41589 bytes)
     
      / a = 180° - 30°  
                      2
    (Base angles of isosceles triangle)
    = 150° ÷ 2
    = 75° 

    80° + / b = 180° ( Interior angles, BD // GE )
    / b = 180° - 80° 
    = 100°