2014 - WAEC Mathematics Past Questions and Answers - page 5

if m + n = 120^o and n + r = 100^o

then m + n = 120^o

then r = 180^o - 120^o = 60^o

also n + r = 100^o

m = 180^o = 80^o

m + r is = 80^o + 60^o

= 140^o

From the diagram SR//UW given that < RSV = 45^o and < WVT = x^o

< WVT = 45^o(corresponding angle)

x^o = 45

x^o + z^o = 180^o (sum of < on str. line)

45^o + z^o = 180^o

z^o = 180^o - 45^o

z = 135^o

z + y^o + 20^o = 180^o (sum of < s in \(\bigtriangleup\))

135^o + y^o + 20^o = 180^o

y^o + 155^o = 180^o

y^o + 180^o - 155^o

y^o = 25^o

< URT = < TRQ (angle alternate a tangent and a chord equal to angle in the alternate segment)

< RUT = x^o

In \(\bigtriangleup\) URT

< RUT + < RUT + < UTR = 180^o (sum of int. < s of \(\bigtriangleup\))

< URT + x + x = 180^o

< URT = 180^o - 2x

Construction: draw a line from Q to point P and another line from S to point P.

< SOQ = 2< QPS (< at centre is twice < on the circumference)

< QPS \(\frac{86}{2} = 43\)

< SQR = < QPS ( < between a chord and tangent = < in the alternate segment)

< SQR = 43^o