(a) In the diagram, BA is parallel to DE. Find the value of x. (b)...
MATHEMATICS
WAEC 1993
(a)
In the diagram, BA is parallel to DE. Find the value of x.
(b) Illustrate graphically and shade the region in which inequalities \(y - 2x < 5 ; 2y + x \geq 4 ; y + 2x \leq 10\) are satisfied.
Explanation
(a)
Draw RC produced to E parallel to DE.
\(\therefore < BCR = 52°\) (alternate angles BA//RC)
also < RCD = 48° (alternate angles RC//DE)
\(x° = 360° - (52° + 48°) = 360° - 100° = 260°\) (angles at a point = 360°)
(b) \(y - 2x < 5 ... (i)\)
\(2y + 2x \geq 4 \implies y + x \geq 2 ... (ii)\)
\(y + 2x \leq 10 ... (iii)\)
From (i), if \(y - 2x = 5\), when x = 0, y = 5, when x = 2, y = 9.
From (ii), if \(y + x = 2\). when x = 0, y = 2, when x = 3, y = -1
From (iii), if \(y + 2x = 10\), when x = 0, y = 10, when x = 2, y = 6.
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