WAEC Mathematics Past Questions & Answers - Page 70

346.

The figure is a pie chart which represents the expenditure of a family in a year. If the total income of the family was Le 10,800,000.00, how much was spent on food?

Le 2,250,000.00

Le 22,700,000.00

Le 3,600,000.00

Le 4,500,000.00

View answer & explanation

Correct answer is C

sectoral angle representing food

= 360^o - (80 + 70 + 90)^o

= 120^o

Amount spent on food

= \(\frac{\tect{sectoral angle}}{360^o}\) x Le 10,800,000

= Le 3,600,000

347.

In the diagram, TX is perpendicular to UW, |UX| = 1cm and |TX| = |WX| = \(\sqrt{3}\)cm. Find UTW

135^o

105^o

75^o

60^o

View answer & explanation

Correct answer is C

In \(\Delta\) UXT, tan\(\alpha\) = \(\frac{1}{\sqrt{3}}\)

\(\alpha\) = tan^-1(\(\frac{1}{\sqrt{3}}\))

= 30^o

In \(\Delta\)WXT, tan\(\beta\) \(\frac{\sqrt{3}}{\sqrt{3}}\) = 1

\(\beta\) = tan^-1(1) = 45^o

Hence, < UTW = \(\alpha\) + \(\beta\)

= 30^o + 45^o = 75^o

348.

In the diagram, PR||SV||WY|, TX||QY|, < PQT = 48^o and < TXW = 60^o.Find < TQU.

120^o

108^o

72^o

60^o

View answer & explanation

Correct answer is C

In the diagram, < TUQ + 60^o(corresp. angles)

< QTU = 48^o (alternate angles)

< QU + 60^o + 48^o = 180^o(sum of angles of a \(\Delta\))

< TQU = 180^o - 108^o

= 72^o

349.

In the diagram, TS is a tangent to the circle at S. |PR| and < PQR = 177^o. Calculate < PST.

54^o

44^o

34^o

27^o

View answer & explanation

Correct answer is A

In the diagram above, x₁ = 180^o - 117^o = 63^o(opposite angles of a cyclic quad.)

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

x₁ + x₂ + \(\alpha\) = 180^o (sum of angles of a \(\Delta\)

63^o + 63^o + \(\alpha\) = 180^o

\(\alpha\) = 180^o - (63 + 63)^o

= 54^o