WAEC Past Questions and Answers - Page 2667

13,331.

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

13,332.

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

13,333.

\(\begin{array}{c|c}
Age(years) & 13 & 14 & 15 & 16 & 17 \\
\hline
Frequency & 10 & 24 & 8 & 5 & 3
\end{array}\)
Find the median age

View answer & explanation

Correct answer is B

Median = \(\frac{N}{2}\)th age

= \(\frac{50}{2}\)th age

= 25th age

= 14 years

13,334.

\(\begin{array}{c|c}
Age(years) & 13 & 14 & 15 & 16 & 17 \\
\hline
Frequency & 10 & 24 & 8 & 5 & 3
\end{array}\)

The table shows the ages of students in a club. How many students are in the club?

View answer & explanation

Correct answer is A

Number of students in the club is

10 + 24 + 8 + 5 + 3 = 50

13,335.

If cos \(\theta\) = x and sin 60^o = x + 0.5 0^o < \(\theta\) < 90^o, find, correct to the nearest degree, the value of \(\theta\)

32^o

40^o

60^o

69^o

View answer & explanation

Correct answer is D

sin 60^o = x + 0.5 0^o(given)

0.8660 = x + 0.5

0.8660 - 0.5 = x

x = 0.3660

cos\(\theta\) = x(given)

cos\(\theta\) = 0.3660

Hence, \(\theta\) = cos^-1(0.3660)

= 68.53^o

= 69^o (nearest degree)