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Angles Revision


We have seen a number of definitions and introduced quite a bit of new language in Geometry so far.  Let us revise what we know and practise this a little before moving on to some new work.  

Line Definitions


Line: passes through two points and extends to infinity in both directions, notated  

Line segment: starts at a point and ends at a point, notated 

Ray: starts at a point and extends through a second point to infinity, notated 

Angle Definitions


Acute: an angle measuring between $0^\circ$0° and $90^\circ$90°

Right: an angle measuring exactly $90^\circ$90° 

Obtuse: an angle measuring between $90^\circ$90° and $180^\circ$180°

Straight: an angle measuring exactly $180^\circ$180° 

Reflex: an angle measuring between $180^\circ$180° and $360^\circ$360°

Revolution: an angle measuring exactly $360^\circ$360°

Labelling angles

An angle is made by two lines joining at an APEX. We label an angle by moving from a point on one line (line, segment or ray), through the APEX to a point on the the other line (line, segment or ray).  

Angle rules and definitions

Angles at a Point: Angles at a point sum to  $360^\circ$360°

Angles on a line: Adjacent angles on a straight line are supplementary (add up to $180^\circ$180°)

Supplementary Angles: Sum to $180^\circ$180°

Complementary Angles: Sum to $90^\circ$90°

Vertically Opposite Angles

Vertically opposite angles are equal.  

(To help remember this, it is sometimes referred to as the X rule).  

Worked Example

Question 1

In the following, state the vertex and name the angle.

Question 2

Is the angle acute, obtuse or reflex?

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