2021 WAEC Mathematics Theory In the diagram, PQRS is a circle. \(\overline{|PQ|}\) = \(\overline{|QS|}\). &ang;SPR = 26° and the...

In the diagram, PQRS is a circle. \(\overline{|PQ|}\) = \(\overline{|QS|}\). ∠SPR = 26° and the interior angles of PQS are in the ratio 2:3 :3.

Calculate: (i) PQR; (ii) RPQ; (iii) PRQ

(b) The coordinates of two points P and Q in a plane are (7, 3) and (5, x) respectively, where X is a real number.

If |PQ| = 29units, find the value of x.

(a)(i) ∠PSQ = ∠QPS

∠PQS = \(\frac{2}{8}\) x 180°

=45°

∠SPQ = ∠PSQ

= \(\frac{3}{8}\) x 180 = 67.5°

∠SQR = ∠SPR= 26°

∠PQR = ∠PQS + ∠SQR

= 45°+ 26°

= 71°

(ii) ∠RPQ = ∠SPQ - ∠SPR

= 67.5°- 26°

= 41.5°

(iii) ∠PRQ = 180° - 41.5° - 71°

= 67.5°

(b) √29 = √{ (7 - 5)\(^2\) + (3-x)\(^2\)}

√29 = √{ 2\(^2\) + (3 - x)\(^2\)}

29 = 4 + (3 - x)\(^2\)

25 = (3 - x)\(^2\)

x\(^2\) -6x - 16

(x + 2)(x - 8) = 0

x = -2 or 8

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