WAEC - Mathematics (2000 - No. 26)

In the diagram, POS and ROT are straight lines, OPQR is a parallelogram. |OS| = |OT| and ∠OST = 50°. Calculate ∠OPQ.

160^o

140^o

120^o

100^o

< T = < S = 50° (OS = OT)

< SOT = 180° - 2(50°) = 80°

< ROP = 80° (vertically opposite angle)

\(\therefore\) < OPQ = 180° - 80° = 100° (adjacent angles)