Higher June 2024 Paper 2 Q17
17 \(AB\) is a straight line.
Both angles are given in degrees.
Not drawn accurately
By working out the value of \(x\),
work out the ratio smaller angle : larger angle [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{1}{4}x + 15 + \dfrac{2}{3}x - 44 = 180\) | M1 | oe equation |
| \(\dfrac{1}{4}x + \dfrac{2}{3}x = 180 - 15 + 44\) or \(3x + 180 + 8x - 528 = 2160\) | M1dep | oe equation with terms collected eg \(\dfrac{11}{12}x = 209\) or oe equation with fractions eliminated eg \(11x = 2508\) |
| \((x =)\ 209 \div \dfrac{11}{12}\) or \((x =)\ 228\) | M1dep | oe calculation that leads to \((x =)\ 228\) eg \((x =)\ 2508 \div 11\) implied by 72 and 108 |
| 72 : 108 | A1 | oe ratio eg 2 : 3 or 1 : 1.5 or \(\dfrac{2}{3}\) : 1 |
Additional guidance
| Ignore simplification attempt after correct ratio seen eg 72 : 108 in working with answer 36 : 52 | M3A1 |
| Accept [0.66, 0.67] for \(\dfrac{2}{3}\) | |
| Accept [0.91, 0.92] for \(\dfrac{11}{12}\) | |
| Accept [1.09, 1.1] for \(\dfrac{12}{11}\) |