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0580 P41 - Jun 2013 - Q8 - 15 marks
15873
Pentagonangles11011084xx withsymmetry

In pentagon ABCDE, EAB = ABC = 110°, CDE = 84°, BCD = DEA = x°.

(a(i)) Find x. [2]

(a(ii)) BC = CD. Find CBD. [1]

(a(iii)) The pentagon also has one line of symmetry. Find ADB. [1]

Circle minorAOC3y circumferenceABC4yplus4

(b) A, B, C lie on a circle centre O. The marked non-reflex AOC is 3y°, and ABC = (4y + 4)°. Find y. [4]

CyclicquadrilateralPQRS SPQ78 PRdiagonal

(c(i)) In cyclic PQRS, SPQ = 78°. Give the reason QRS = 102°. [1]

(c(ii)) PRQ : PRS = 1 : 2. Find PQS. [3]

Two similarfiguresareas5and7.2 basesland6.9

(d) The figures have areas 5 cm² and 7.2 cm² and corresponding bases l cm and 6.9 cm. Find l. [3]

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