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Shape, Space and Measure (Intermediate) - Angle Properties

There are a number of properties of angles in certain situations.

Angles On a Straight Line

Angles which are next to each other on a straight line add up to 180^o. This is shown in the diagram below.

angle properties1

Angle a + Angle c =180^o

Using this property we can solve problems involving missing angles.

For Example:

Given the diagram above, with only one of the angles given, calculate the missing angle. a^o = 70^o , Calculate angle c.

70 + c = 180 (Angles on a straight line)
c = 180 – 70 = 110^o

Angles at a Point

Angles meeting at a point add up to 360^o. In the diagram below:


Again, this property can be used to solve problems.
For Example:
1) In the diagram above, if three of the angles are given, then the missing angle is found by adding the three angles together and subtracting from 360. Angles AED, BEC, and AEB are equal to 30^o, 30^o and 150^o respectively. Calculate angle DEC.
Angle DEC = 360 – (30+30+150) = 360 – 210 = 150^o

2) In the diagram below, the three angles given are, 90, 90 and 41. Calculate angle e.

Angle e = 360-(41+90+90) = 139^o

Vertically Opposite Angles
When two straight lines cut, forming an X shape, then the opposite angles are equal. In the diagram below:

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