Question

4. In Fig. 6.42, if lines PQ and RS intersect at point T, such that Z PRT = 40°, ZRPT=95° and ZTSQ = 75°, find Z SQT. 2​

Answer 1

Answer:

In PRT

By angle sum property of triangle

∠PRT+∠RPT+∠PTR= 180  

⇒90+45+∠PTR= 180  

⇒135 +∠PTR= 180  

⇒∠PTR= 180−135  

⇒∠PTR= 45

Now,

∠STQ=45  (vertically opposite angles)

In ΔSQT

By angle sum property of triangle  

∠SQT+∠STQ+∠TSQ= 180  

∠SQT+75+45= 180  

∠SQT+120= 180  

∠SQT= 180 −120  

∠SQT= 60.