Foundation November 2024 Paper 1 Q18
18. In the diagram below, ABC is an isosceles triangle and DA is a straight line.
Diagram not drawn to scale
Show that \(x = 255\).
You must give a reason for each step of your answer. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (\(B\hat{A}C\) or \(A\hat{B}C\) =) \(\dfrac{180 - 50}{2}\) = 65(°) AND (\(x\) =) 360 – 40 – 65 = 255(°) OR (\(B\hat{A}C\) =) 360 – 40 – 255 = 65(°) AND (\(A\hat{B}C\) =) 180 – 65 – 50 = 65(°) | B2 | B1 for \(B\hat{A}C\) = 65(°) or \(A\hat{B}C\) = 65(°). May be seen on diagram for B1. |
| A correctly explained solution. (\(B\hat{A}C\) =) 65(°) Base angles in an isosceles triangle are equal (\(x\) =) 255(°) Angles around a point add up to 360°. OR starting with the 255(°) (\(B\hat{A}C\) =) 65(°) Angles around a point add up to 360°. (\(A\hat{B}C\) =) 65(°) Base angles in an isosceles triangle are equal | E2 | E2 and E1 dependent on B2 being awarded. E1 for ‘base angles in an isosceles triangle are equal’ |
| (4) |