1MA0 Foundation June 2013 Paper 2 Q20
*20
Diagram NOT accurately drawn
DAC, FCB and ABE are straight lines.
Work out the size of the angle marked \(x\).
You must give reasons for your answer. (5)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| (Method 1) Angle ACB = 180 – 135 (= 45) (sum of angles on a straight line = 180) Angle ABC = 180 – 70 – 45 (=65) (sum of angles in a triangle = 180) (x =) 180 – 65 (=115) (sum of angles on a straight line = 180) OR (Method 2) Angle ACB = 180 – 135 (= 45) (sum of angles on a straight line = 180) (x =) 70 + 45 (=115) (exterior angle = sum of interior opposite angles) OR (Method 3) Angle DAB = 180 – 70 = 110 (sum of angles on a straight line = 180) (x =) 360 – 135 – 110 (sum of exterior angles of a polygon = 360) | \(x = 115\) | 5 | M1 for correct method to find angle DAB or angle ACB or angle ABC (may be implied by correct angle marked in diagram) M1 for complete correct method to find \(x\) A1 for \(x = 115\) C2 (dep on M1) for fully correct reasons for chosen method no extras (C1 (dep on M1) for one correct reason for chosen method) [NB \(x = 115\) must be stated explicitly, 115 only scores A0] |