Mathematics

Mathematics

Problem

Draw a convex quadrilateral PQRSPQRS. Join the diagonal PRPR. a. (i) Write a paragraph proof to show that the sum of the interior angles of △PQR\triangle PQR is 180∘180^{\circ}. b. (ii) Using part (i) and a similar argument for △PRS\triangle PRS, prove that ∠P+∠Q+∠R+∠S=360∘\angle P+\angle Q+\angle R+\angle S = 360^{\circ} for any convex quadrilateral. c. (iii) If ∠P=95∘\angle P = 95^{\circ}, ∠Q=88∘\angle Q = 88^{\circ} and ∠R=102∘\angle R = 102^{\circ}, find ∠S\angle S with reasons.

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