WAEC Mathematics Past Questions & Answers - Page 71

351.

In the diagram, O is the centre of the circle, < XOZ = (10cm)^o and < XWZ = m^o. Calculate the value of m.

Correct answer is A

In the diagram above, \(\alpha\) = 2m^o (angle at centre = 2 x angle at circumference)

\(\alpha\) + 10m^o = 360^o (angle at circumference)

\(\alpha\) + 10m^o = 360^o(angles round a point)

2m^o + 10m^o = 360^o

12m^o = 360^o

m^o = \(\frac{360^o}{12}\)

= 30^o

352.

In the diagram, \(\bar{PF}\), \(\bar{QT}\), \(\bar{RG}\) intersect at S and PG||RG. If < SPQ = 113^o and < RSt = 220, find < PSQ

22^o

45^o

67^o

89^o

View answer & explanation

Correct answer is B

In In the diagram given, \(\alpha\) = 22^o (vertically opp. angles), \(\alpha\) = \(\beta\) (alternate angles)

< PSQ + 133^o + \(\beta\) = 180^o (sum of angles of a \(\Delta\))

< PSQ + 133^o + 22^o = 180^o

< PSQ = 180^o - (133 + 22)^o

45^o

353.

In the diagram, \(\bar{YW}\) is a tangent to the circle at X, |UV| = |VX| and < VXW = 50o. Find the value of < UXY.

70^o

80^o

105^o

110^o

View answer & explanation

Correct answer is B

In the diagram above, x1 = 50(angles in alternate segment)

x1 = x2(base angles of isos. \(\Delta\))

< UXY + x2 + 50o = 180o(sum of angles on a straight line)

< UXY + 50o + 50o = 180p

< UXY + 100o = 180o

< UXY = 180o - 100o

= 80o