Intermediate June 2017 Unit 1 Q7
7. ABCD is a quadrilateral.
Diagram not drawn to scale
(a) Calculate the value of \(x\). [4]
(b) When ABCD is drawn to scale, would the lines AD and BC be parallel or not?
You must justify your answer without using a scale drawing. [2]
You must justify your answer without using a scale drawing. [2]
| Scheme | Marks | Comments |
|---|---|---|
| x + 2x + 3x + 90 = 360 or equivalent. | M1 | Allow M1 for attempting sum of a + b + c + 90 with ratio a:b:c = 1:2:3 and clearly using trial and improvement to aim for a total of 360. |
| 6x = 270 | A1 | |
| \(x = \dfrac{270}{6}\) | A1 | F.T. from ax = b. |
| = 45 | A1 | Allow SC2 for an answer of 15 (from ‘= 180’) |
| Scheme | Marks | Comments |
|---|---|---|
| Correct use of 2x = 90(°) | B1 | F.T. ‘their value of x’. Must be used in justification. |
| ‘Yes’ AND correct justification. e.g. ‘Yes because of interior angles’, ‘Yes as lines are perpendicular to the base’ ‘Both A and B are 90’. | E1 | Dependent on B1 with F.T. justification. Alternative method for the B1 mark Use of 3x = 135(°) AND x = 45(°) |