Higher June 2022 Paper 2 Q20
20 \(A\), \(B\), \(C\) and \(D\) are points on the circumference of a circle, centre \(O\).
\(ADE\) and \(BCE\) are straight lines.
Work out the size of angle \(CDE\).
Give a reason for each stage of your working. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 98 | M1 | for \(BAD = 132 \div 2\ (= 66)\) |
| M1 | eg \(BCD = 180 - \text{``}66\text{''}\ (= 114)\) or \(ABE = 180 - \text{``}66\text{''} - 16\ (= 98)\) M2 for reflex \(BOD = 360 - 132\ (= 228)\) and \(BCD = \text{``}228\text{''} \div 2\ (= 114)\) | |
| A1 | for finding \(CDE = 98\) | |
| C1 | (dep on at least M2) for one circle theorem relevant to their method eg The angle at the centre of a circle is twice the angle at the circumference or Opposite angles of a cyclic quadrilateral add up to 180 |
Additional guidance
Angles may be seen on diagram
Underlined words need to be shown; reasons need to be linked to their method.