WAEC Mathematics Past Questions & Answers - Page 57

Length of arc, L = 21.4 - 2 x 4.2cm

= 21.4 - 8.4

= 13cm

But L = $\frac{\theta}{360^o}$ x 2$\pi r$

i.e 13 = $\frac{\theta}{360^o}$  x 2 x $\frac{22}{7}$ x 4.2

= 13 x 360$^o$ x 7

= $\theta$ x 2 x 22 x 4.2

$\theta$ = $\frac{13 \times 360^o \times 7}{44 \times 4.2}$

= $\approx$ 177.27$^o$

$\approx$ 177$^o$ (to the nearest degree)

Total donation = 4 x 500 + 7 x 2000 + 20 x 1000 + 9 x 700 + 4 x 500 + 5 x 100 + 3 x 50 + 1 x 2 + 2 x 10 = 20000 + 14000 + 20000 + 6300 + 2000 + 500 + 150 + 2 + 20 = N62,972

m + n = 110$^o$, (n + r) = 130$^o$

(m + n) = 120$^o$

then, r = 130$^o$ - n

and;

m + (130^o - n) = 120$^o$

m - n = -10$^o$

2m + (n + r) = 110 + 120 = 230

2m + 130 = 230

2m = 230 - 130

m = $\frac{100}{2}$ = 50$^o$

n = 110$^o$ - 50$^o$

= 60$^o$

r = 130$^o$ - 60$^o$ = 70$^o$

Hence, the ratio m : n : r

= 50 : 60 : 70

= 5 : 6 : 7

In the diagram,

a = z (alternate angles)

b = 180$^o$ - a (angles on a straight line)

b = 180$^o$ - z

c = 180$^o$ - x (angles on a straight line)

y = b + c (sum of oposite interior angles)

y = 180$^o$ - z + 180$^o$ - x

y = 360$^o$ - z - x

x = 360$^o$ - y - z

In the diagram, < WOZ = 180$^o$ (angle on a straight line)

< WOX = < XOY = < YOZ

(|WX| = |XY| = |YZ|)

$\frac{180^o}{3}$ = 60$^o$

= 60$^o$

M + m =2m (base angles of isosceles $\bigtriangleup$, |OY| and |OZ| are radii)

< YOZ + 2m (base angles of a $\bigtriangleup$)

60$^o$ + 2m = 180$^o$ (sum of a $\bigtriangleup$)

60$^o$ + 2m = 180$^o$

2m = 180$^o$ - 60$^o$

2m = 120$^o$

m = $\frac{120^o}{2}$

= 60$^o$