Angle Sum Properties (Line, Around a Point)

When two rays form a straight line, the angle between them is a straight angle. A straight angle measures \(180^\circ\). This gives us the first important angle sum fact:

The angles on a straight line add up to \(180^\circ\).

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(Angle 1 + Angle 2 = 180°)

If one of the angles on a straight line is known, the other can be found by subtracting from \(180^\circ\). This simple idea appears often in geometry problems.

A linear pair is formed when two adjacent angles lie on a straight line. Since their non-common arms form a straight angle, the two angles in a linear pair must be supplementary, meaning:

Sum of angles in a linear pair = \(180^\circ\)

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The two angles on either side of the common arm together form a half-turn of \(180^\circ\).

When several angles meet at a single point, they form a full turn around that point. A full turn measures \(360^\circ\).

So, the second major angle sum property is:

The angles around a point add up to \(360^\circ\).

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    / | ) 60°
 120° | 
     \|  ) 180°
      +

No matter how many angles meet at a point, if they complete one full rotation, their total will always be \(360^\circ\).

These angle sum rules are extremely useful when working with diagrams:

• If two angles sit on a straight line, their sum is \(180^\circ\).
• If angles form a complete turn at a point, their sum is \(360^\circ\).
• Linear pairs are just a special case of straight-line angles.

Real-life examples include a rotating fan (angles around a point) and the angles made by a table lamp when its arm rotates on a fixed base (angles on a straight line). Understanding these ideas makes many geometry constructions and angle calculations simpler.