JAMB - Mathematics (1980 - No. 42)

In the figure, If PT is parallel to RS, PQ = PT, and angle SQT = 90o, Find x

35^o

50^o

55^o

70^o

80^o

from the diagram above, angle b = 180º - 55º - x ( 55º not 56º)

sum of angle at Q = y + 90º + 180º - 55º - x = 180º( sum of angles on a straight line)

y - x = -35 ..................................... eq1

sum of angle in triangle TPQ = 180º - x + 2y = 180º ( sum of angles in a triangle )

2y - x = 0 ............................................eq2

solving eq1 and eq 2 simultaneously

x = 70º