2014 - WAEC Mathematics Past Questions and Answers - page 5
if m + n = 120o and n + r = 100o
then m + n = 120o
then r = 180o - 120o = 60o
also n + r = 100o
m = 180o = 80o
m + r is = 80o + 60o
= 140o
From the diagram SR//UW given that < RSV = 45o and < WVT = xo
< WVT = 45o(corresponding angle)
xo = 45
xo + zo = 180o (sum of < on str. line)
45o + zo = 180o
zo = 180o - 45o
z = 135o
z + yo + 20o = 180o (sum of < s in (\bigtriangleup))
135o + yo + 20o = 180o
yo + 155o = 180o
yo + 180o - 155o
yo = 25o
< URT = < TRQ (angle alternate a tangent and a chord equal to angle in the alternate segment)
< RUT = xo
In (\bigtriangleup) URT
< RUT + < RUT + < UTR = 180o (sum of int. < s of (\bigtriangleup))
< URT + x + x = 180o
< URT = 180o - 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 = 43o