In the fig. 1.2, two straight
lines PQ and RS intersect each
other at O. If angle POT = 75° find
the value of angle QOS,angle SOT, angle POR
and angle ROQ
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Step-by-step explanation:
When two straight lines intersect, vertically opposite angles are equal.
therefore,
a = 4b...(i), 2c = b + 75 ..(ii)
Since, angle around a point = 360°
therefore,
a + 2c + 4b + 75 + b = 360
= 4b + (b + 75) + 4b + 75 + b = 360
= 10b + 150 = 360
= 10b = 210
= b = 21
a = 4b = 4×21 = 84
2c = 75 + b = 75 + 21 = 96
Hence,
Angle QOS = a = 84°
Angle SOT = b = 21°
Angle POR = 4b = 84°
Angle ROQ = 2c = 96°
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