WAEC - Mathematics (1991 - No. 44)

In the diagram above, ∠PTQ = ∠URP = 25° and XPU = 4URP. Calculate ∠USQ.

100^o

120^o

125^o

130^o

150^o

Since < URP = 25°, then < XPU = 4 x 25° = 100°

\(\therefore\) < TPQ = 180° - 100° = 80°

\(\therefore\) < PQT = 180° - (80° + 25°) = 75°

< SQR = 75° - 25° = 50° (exterior angle = 2 opp interior angles)

\(\therefore\) < USQ = 180° - 50° = 130°