Theory question 104
Sets(a) Out of 30 candidates applying for a post, 17 have degrees, 15 diplomas and 4 neither degree nor diploma. How many of them have both?
(b) In triangle PQR, M and N are points on the sides PQ and PR respectively such that MN is parallel to QR. If ∠PRQ = 75°, PN = QN and ∠PNQ = 125°, determine (i) ∠NQR; (ii) ∠NPM.
Show the model answer
Model answer
(a) 30 − 4 = 26 have at least one. Both = 17 + 15 − 26 = 6.
(b)(i) PNR is a straight line, so ∠QNR = 180° − 125° = 55°. In ΔNQR: ∠NQR = 180° − 55° − 75° = 50°.
(ii) ΔPNQ is isosceles (PN = QN), so ∠NPQ = ∠NQP = (180° − 125°)/2 = 27.5°. M is on PQ, so ∠NPM = 27.5°.
Explanation
Use n(D ∪ Dip) = n(D) + n(Dip) − n(both).