Math, asked by yudonthelpme, 1 month ago

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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Answers

Answered by rakeshdubey33
0

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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