Theory question 108
Triangles and Quadrilaterals(a) In the diagram, ∠KLM = x, ∠LMK = y, ∠KJH = r and ∠KGF = 110°. If 2x = r = y, find the value of x.
(b) Ten boys and twelve girls collected donations for a project. The total amount colected by the boys was N600.00 greater than that collected by the girls. If the average collection of the boys was N100.00 greater than the average collection of the girls, how much was collected by the two groups?
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(a) ∠KGJ = 180° − 110° = 70°
∠JKM = x + y (exterior angle of triangle KLM)
In triangle JKG: r + (x + y) + 70° = 180°
With r = y = 2x: 2x + x + 2x = 110° → x = 22°
(b) Let the girls collect N g; boys collect N(g + 600)
(g + 600)/10 = g/12 + 100 → 6(g + 600) = 5g + 6000 → g = 2400
Girls N2,400, boys N3,000; together N5,400
Use the exterior angle of a triangle twice in (a).