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Angle Properties

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. Angle a = 70^o. Calculate angle c.

70^o+ c = 180^o (angles on a straight line)
c = 180^o – 70^o = 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.
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^o.
Angles AÊD, BÊC, and AÊB are equal to 30^o, 30^o and 150^o respectively. Calculate angle DÊC.
Angle DÊC = 360^o – (30^o + 30^o + 150^o) = 360^o – 210^o = 150^o

Example 2: In the diagram below, the three angles given are 90^o, 90 ^oand 41^o. Calculate angle e.

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