Q 14 In the given figure, O is the centre of the circle Find the value of x - Maths - Circles

Question

Q 14 In the given figure, O is the centre of the circle Find the
value of x

Shruti Tyagi · Accepted Answer

Dear Student,

Construction : Join OCnow OC=OB=OA  as these are radius of circleIn △OCBOC=OB ⇒∠OCB=∠OBC=20°  --angle opposite to equal sides are equalnow sum of all angles of triangle=180⇒∠OCB+∠OBC+∠BOC=180⇒20+20+∠BOC=180⇒∠BOC=180-40⇒∠BOC=140Similarly In △OCAOC=OA⇒∠OCA=∠OAC=50°  --angle opposite to equal sides are equalnow sum of all angles of triangle=180⇒∠OCA+∠OAC+∠AOC=180⇒50+50+∠BOC=180⇒∠AOC=180-100⇒∠AOC=80Sum of all angles across the centre is 360Hence ∠BOC+∠AOC+∠BOA=360⇒140+80+x=360⇒x=360-220⇒x=140

Regards,

Q.14. In the given figure, O is the centre of the circle. Find the value of x.