In the diagram, PQRS is a circle. \(\overline{|PQ|}\) = \(\overline{|QS|}\). ∠SPR = 26° and the...
MATHEMATICS
WAEC 2021
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.
Explanation
(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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