O-LevelMathematicsGeometry4024/22 · May/June 2023 · Q38 Marks
(a) [Figure 3.1] The diagram shows the equilateral triangle B and part of the regular polygon A which have a common side. The interior angle of polygon A is 165°. (b) [Figure 3.2] A, B and C are points on the circumference of a circle, centre O. Angle ABC = x°.
- (a)(i)Find the value of y.[1]
- (a)(ii)Calculate the number of sides of polygon A.[2]
- (b)(i)Show that angle OAC = (90 - x)°. Give reasons for your answer.[3]
- (b)(ii)Angle BAO = 54° and angle OCB = 11°. Find the value of x.[2]
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Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [1] 135
- [2] M1 for 180(n-2)/n [=165] oe or [n =] 360/(180-165) oe
- or B1 for exterior angle = 15
- 24
- [3] B2 for angle AOC = 2x and angle AOC is angle at centre is twice angle at circumference OR
- B1 for angle AOC = 2x
- B1 for angle OAC = (180-their2x)/2 and isosceles triangle
- B1 for angle AYC = x angles in same segment are equal
- B1 for angle YCA = 90 angles in a semicircle
- B1 for angle OAC = 90 - x angles in a triangle
- [2] B1 for angle BCA = 90 – x – 11 oe or angle OBC = 11 or angle BDA = 180 – 54 – x oe or angle ADC = x + 54 oe or angle ODC = 180 – 2x – 11 oe or M1 for a correct equation
- 43
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