MATHS REVISION ANGLES AND LOCI

ANGLE BASICS

acute angles : sharp and pointy angles which are less than 90` 

obtuse angles : wider angles (between 90` and 180`)

right angles : square corners(90`)

DRAWING ANGLES WITH A PROTRACTER :

1. Draw a base line 

2.if the angle is an acute angle then you can make sure the protractor's 0 is facing inwards.

3. if it is a small angle use the outside scale.

GEOMETRY RULES:

1. Angles in a triangle = 180' -- a+b+c=180'

2. Angles on a straight line add upto 180`-- a+b+c=180'

3. Angles in a quadrilateral add up to 360' -- a+b+c+d=360'

4. Angles round a point = 360'

5.Exterior angle of a triangle = sum of opposite interior angles. a+b=d

6. Isosceles triangles have 2 sides the same and 2 angles the same .

PARALLEL LINES 

Alternate angles: alternate angles are the same they are found in a Z shape.

Vertically opposite angles : vertically opposite angles add up to 180' they are found in a C or U shape

Corresponding Angles: corresponding angles are the same.They are found in an F shape.

Example ; find the angle x 

There is a corresponding angle that is 115' what is x ?

Its the same !

INTERIOR AND EXTERIOR ANGLES

For any polygon (regular or irregular)

sum of exterior angles =360'

interior angles =180' - exterior angles

for regular polygons only : exterior angles = 360/n (number of sides)

SUM OF INTERIOR ANGLES

the formula for all polygons: SUM OF ANGLES= (n-2x180')

 E.G For a pentagon. pentagon = 5 sides

Sum of interior angles=(5-2)x180'=540'

REVISON SUMMARY QUESTIONS: 

1. Give an example of an acute angle, obtuse and reflex angle (3)

2. What do the angles in a quadrilateral equal to?                       (1)

3. What type of angles do you find a Z shape on parallel lines?   (1)

4.Work out the size of an exterior angle and an interior angle of a        regular decagon (10 sided shape)                                                    (2)

5.What is the sum of the interior angles in a hexagon and heptagon (2)