2026 YTSS P2 Q7

2026 YTSS P2 Q7

Secondary 4
10 marks
  1. \(A,B,C\) and \(E\) are four vertices of an \(n\)-sided polygon and reflex angle \(ABC\) is \(190^\circ\).
    The remaining reflex angles of the \(n\)-sided polygon are each equal to \(205^\circ\).
    A regular pentagon \(CDEFG\) is placed such that one of its diagonals, \(CE\), is also one of the sides of the \(n\)-sided polygon.
    1. Find \(\angle BCD\).[3]
    2. Find the number of sides of the \(n\)-sided polygon.[3]
  2. In the diagram below, \(AB,CD\) and \(EF\) are parallel lines. \(XWV\) and \(XYZ\) are straight lines.
    The line \(XZ\) bisects angle \(BXW\) and \(\angle VWY=106^\circ\).
    1. Show that \(WXY\) is an isosceles triangle. Give reasons for your working.[2]
    2. Which is the longest side of triangle \(XVZ\)? Show all your necessary workings.[2]

Solution:

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Answer:(a)(i) \(119^\circ\) (ii) 15 sides. (b)(i) \(WX=WY\) (shown) (ii) \(XZ\), opposite \(74^\circ\).

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