In the figure (ii) given below, O is the center of the circle. If ∠AOB = 140° and ∠OAC = 50°, find (i) ∠ACB (ii) ∠OBC (iii) ∠OAB (iv) ∠CBA.

(i) From figure, ⇒ ∠AOB + Reflex ∠AOB = 360° ⇒ 140° + Reflex ∠AOB = 360° ⇒ Reflex ∠AOB = 360° - 140° ⇒ Reflex ∠AOC = 220°. Arc AB subtends Reflex ∠AOB at center and ∠ACB at point C of circle. ⇒ Reflex ∠AOB = 2 ∠ACB ⇒ 2∠ACB = 220° ⇒ ∠ACB = ⇒ ∠ACB = 110°. Hence, the value of ∠ACB = 110°. (ii) In Quadrilateral OABC, ⇒ ∠OAC + ∠ACB + ∠BOA + ∠OBC = 360° ⇒ 50° + 110° + 140° + ∠OBC = 360° ⇒ 300° + ∠OBC = 360° ⇒ ∠OBC = 360° - 300° ⇒ ∠OBC = 60° Hence, the value of ∠OBC = 60°. (iii) In △OAB, OA = OB (Radius of the circle) ∠OAB = ∠OBA = x (∵ angles of equal sides in isosceles triangle are equal.) Sum of angles in a triangle are equal, ⇒ ∠AOB + ∠OAB + ∠OBA = 180°. ⇒ 140° + x + x = 180° ⇒ 140° + 2x = 180° ⇒ 2x = 40° ⇒ x = 20°. Hence, the value of ∠OAB = 20°. (iv) ∠CBA = ∠OBC - ∠OBA ⇒ ∠CBA = 60° - 20° ⇒ ∠CBA = 40° Hence, the value of ∠CBA = 40°.

In the figure (ii) given below, O is the center of the circle. Calculate the values of x and y.

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In the figure (i) given below, M, A, B, N are points on a circle having center O. AN and MB cut at Y. If ∠NYB = 50° and ∠YNB = 20°, find ∠MAN and the reflex angle MON.

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In the figure (i) given below, A, B, C and D are points on the circle with center O. Given that ∠ABC = 62°, find
(i) ∠ADC
(ii) ∠CAB

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In the figure (ii) given below, AB is a diameter of the circle whose center is O. Given that ∠ECD = ∠EDC = 32°, calculate
(i) ∠CEF
(ii) ∠COF

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Mathematics

In the figure (ii) given below, O is the center of the circle. If ∠AOB = 140° and ∠OAC = 50°, find
(i) ∠ACB
(ii) ∠OBC
(iii) ∠OAB
(iv) ∠CBA.

Circles

Related Questions

In the figure (ii) given below, O is the center of the circle. Calculate the values of x and y.

In the figure (i) given below, M, A, B, N are points on a circle having center O. AN and MB cut at Y. If ∠NYB = 50° and ∠YNB = 20°, find ∠MAN and the reflex angle MON.

In the figure (i) given below, A, B, C and D are points on the circle with center O. Given that ∠ABC = 62°, find
(i) ∠ADC
(ii) ∠CAB

In the figure (ii) given below, AB is a diameter of the circle whose center is O. Given that ∠ECD = ∠EDC = 32°, calculate
(i) ∠CEF
(ii) ∠COF

Mathematics

In the figure (ii) given below, O is the center of the circle. If ∠AOB = 140° and ∠OAC = 50°, find(i) ∠ACB(ii) ∠OBC(iii) ∠OAB(iv) ∠CBA.

Circles

Related Questions

In the figure (ii) given below, O is the center of the circle. Calculate the values of x and y.

In the figure (i) given below, M, A, B, N are points on a circle having center O. AN and MB cut at Y. If ∠NYB = 50° and ∠YNB = 20°, find ∠MAN and the reflex angle MON.

In the figure (i) given below, A, B, C and D are points on the circle with center O. Given that ∠ABC = 62°, find(i) ∠ADC(ii) ∠CAB

In the figure (ii) given below, AB is a diameter of the circle whose center is O. Given that ∠ECD = ∠EDC = 32°, calculate(i) ∠CEF(ii) ∠COF

In the figure (ii) given below, O is the center of the circle. If ∠AOB = 140° and ∠OAC = 50°, find
(i) ∠ACB
(ii) ∠OBC
(iii) ∠OAB
(iv) ∠CBA.

In the figure (i) given below, A, B, C and D are points on the circle with center O. Given that ∠ABC = 62°, find
(i) ∠ADC
(ii) ∠CAB

In the figure (ii) given below, AB is a diameter of the circle whose center is O. Given that ∠ECD = ∠EDC = 32°, calculate
(i) ∠CEF
(ii) ∠COF