Many lines through one point
Many lines through one point
IP 1
7 marks
\(n\) different straight lines all pass through a point \(O\), where \(n\ge2\). Count only the angles between neighbouring rays around \(O\).
- State, in terms of \(n\), the number of angles formed around \(O\).[1]
- Explain why these angles add up to \(360^\circ\), and why the \(n\) angles on one side of any one of the lines add up to \(180^\circ\).[2]
- Explain why the angles can be arranged in \(n\) pairs of equal angles.[1]
- Five lines pass through \(O\). Going round from one side of one of the lines, the five angles on that side increase by \(6^\circ\) each time. Find the smallest of these angles.[3]
Solution:
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Answer:(a) \(2n\) (b) angles at a point sum to \(360^\circ\); the \(n\) angles on one side of a line form a straight angle (c) vertically opposite angles are equal (d) \(24^\circ\)
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