Question

CIRCLES CHAPTER CLASS 9

Given below is a quadrilateral PQRS in a circle with centre T. What are the measures of angle b and c?​

Answer 1

Given : a quadrilateral PQRS in a circle with centre T

To Find :  Measures of angle b and c

Solution:

An inscribed angle is half of a central angle that subtends the same arc

∠PSQ = ∠PTQ / 2

∠PTQ = 100°

=> ∠PSQ =100° / 2

=> ∠PSQ = 50°  

=> c = 50°

∠PTS + ∠PTQ  = 180°  Linear Pair

=> ∠PTS + 100°  = 180°

=>  ∠PTS    =  80°

∠PRS = ∠PTS / 2

∠PTS =80°

=> ∠PRS = 80° / 2

=> ∠PRS =40°  

=> b = 40°  

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