1MA0 Foundation June 2012 Paper 1 Q21
*21
Diagram NOT accurately drawn
\(ABC\) is a straight line.
\(BD = CD\).
Angle \(BDC = 50^\circ\).
Angle \(ADB = 20^\circ\).
Work out the size of the angle marked \(x\).
Give reasons for your answer. (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| Angle \(DBC = (180 - 50) \div 2\) Base angles of isosceles triangle are equal Angle \(ABD = 180 - 65\) Angles on a straight line add up to 180 \(x = 180 - 20 - 115\) Angles in a triangle add up to 180 OR Angle \(DBC = (180 - 50) \div 2\) Base angles of isosceles triangle are equal \(x = 65 - 20\) Exterior angle of triangle is equal to sum of interior opposite angles OR Angle \(DCB = (180 - 50) \div 2\) Base angles of isosceles triangle are equal \(x = 180 - 50 - 20 - 65\) Angles in a triangle add up to 180 | 45 with reasons | 4 | M1 for \((180 - 50) \div 2\) oe or 65 seen M1 for \(180 - 20 - (180 -\) “65”) or “65” \(- 20\) or \(180 - 50 - 20 -\) ‘65’ oe C2 for \(x\) identified as 45 with full reasons QWC: Reasons clearly laid out with correct geometrical language used (C1 (dep on M1) for one reason QWC: Reasons clearly laid out with correct geometrical language used ) NOTE: \(x = 45\) with no working or without any correct angles marked on the diagram cannot score. |