Angles
When two lines meet at a point the space between is called the angle. This space is the amount of turning from one line to the other.
There are:
360° in a full turn.
180° in a half turn or on a straight line.
90° in a quarter turn, a right angle, shown with a square at the angle.
Angles less than 90° are called acute angles.
Angles between 90° and 180° are called obtuse angles.
Angles greater than 180° are called reflex angles.
Example
Name the angles in the shape.
Calculating the size of angles
Angles inside a right angle add up to 90°.
Example
If b = 50° then 50 + c = 90
Or 90 – 50 = c
c = 40°
Angles on a straight line add up to 180°.
Example
If d = 50° and f = 35°
then 50 + e + 35 = 180
Or 180 – 50 – 35 = e
e = 95°
Angles at a point add up to 360°.
Example
If g = 51°
h = 103°
j = 32° k = 86°
then 51 + 103 + i + 32 + 86 = 360
i = 360 – (51 + 103 + 32 + 86)
i = 360 – (272) = 88°
Question
Calculate the size of angle r.
The angles are on a straight line so they add up to 180°.
r = 180 – (90 + 55)
r = 180 – 145
r = 35°
Question
Calculate the size of the two missing angles that are the same size.
The angles at a point add up to 360°.
2x = 360 – (117 + 25 + 92)
2x = 360 – 234
2x = 126
x = 63°
Pairs of equal angles
When two lines cross, they form vertically opposite angles.
Vertically opposite angles are equal.
When a line cuts through a pair of parallel lines it creates pairs of angles with special properties.
Corresponding angles
Corresponding angles are equal they are in corresponding positions relative to each parallel line.
The lines make an F shape. Notice that the F shape can be upside down or back to front.
Alternate angles
Alternate angles are equal.
The lines make a Z shape which can also be back to front.
Example
Which angle is corresponding to angle a?
Answer: e
Example
Which angle is vertically opposite f?
Answer: h
Example
Which angle is alternate to h?
Answer: b
Question
Find the sizes of angles v and w.
v = 110° (corresponding angles are equal)
w = 70° (angles on a straight line add up to 180°)
Test yourself
More on M1: Geometry and measures
Find out more by working through a topic
- count1 of 9
