JAMB - Mathematics (1979 - No. 43)
In this figure, PQRS is a parallelogram, PS = PT and < PST = 55\(^o\). The size of <PQR is
125o
120o
115o
110o
10o
Explanation
Both pairs of opp. angles are equal
< STP = 55\(^o\) - isosceles angle
< TSR = 55\(^o\) - alternate angle to < STP
Hence, < PSR = 55\(^o\) + 55\(^o\) = 110\(^o\)
\(\therefore\) < PQR = 110\(^o\)
< STP = 55\(^o\) - isosceles angle
< TSR = 55\(^o\) - alternate angle to < STP
Hence, < PSR = 55\(^o\) + 55\(^o\) = 110\(^o\)
\(\therefore\) < PQR = 110\(^o\)