In the figure, O is the center of the circle, ∠AOE = 150°, ∠DAO = 51°. Calculate the sizes of the angles CEB and OCE.
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Question

In the figure, O is the center of the circle, ∠AOE = 150°, ∠DAO = 51°. Calculate the sizes of the angles CEB and OCE.

KnowledgeBoat · Accepted Answer

We know that, Angle at the center is double the angle at the circumference subtended by the same chord. ⇒ Reflex ∠AOE = 2∠ADE ⇒ ∠ADE = Reflex ∠AOE ⇒ ∠ADE = (360° - 150°) ⇒ ∠ADE = = 105°. From figure, ⇒ ∠DAB + ∠BED = 180° [Sum of opposite angles in a cyclic quadrilateral = 180°.] ⇒ ∠BED = 180° - ∠DAB = 180° - 51° = 129°. Also, ⇒ ∠CEB + ∠BED = 180° [As CED is a straight line] ⇒ ∠CEB = 180° - ∠BED = 180° - 129° = 51°. In △ADC, ⇒ ∠ADC + ∠ACD + ∠DAC = 180° ⇒ ∠ADE + ∠ACD + ∠DAO = 180° [From figure, ∠ADC = ∠ADE and ∠DAC = ∠DAO] ⇒ 105° + ∠ACD + 51° = 180° ⇒ ∠ACD = 180° - 105° - 51° = 24°. From figure, ∠OCE = ∠ACD = 24°. Hence, ∠CEB = 51° and ∠OCE = 24°.

Mathematics

In the figure, O is the center of the circle, ∠AOE = 150°, ∠DAO = 51°. Calculate the sizes of the angles CEB and OCE.

Circles

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Mathematics

In the figure, O is the center of the circle, ∠AOE = 150°, ∠DAO = 51°. Calculate the sizes of the angles CEB and OCE.

Circles

Related Questions

In the figure given, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°.Calculate :(i) ∠RNM,(ii) ∠NRM.

In the given figure, SP is the bisector of ∠RPT and PQRS is a cyclic quadrilateral. Prove that :SQ = SR.

In the figure, given below, P and Q are the centers of two circles intersecting at B and C. ACD is a straight line. Calculate the numerical value of x.

The figure shows two circles which intersect at A and B. The center of the smaller circle is O and lies on the circumference of the larger circle. Given ∠APB = a°.Calculate, in terms of a°, the value of :(i) obtuse ∠AOB,(ii) ∠ACB,(iii) ∠ADB.Give reasons for your answers clearly.

In the figure given, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°.
Calculate :
(i) ∠RNM,
(ii) ∠NRM.

In the given figure, SP is the bisector of ∠RPT and PQRS is a cyclic quadrilateral. Prove that :
SQ = SR.

The figure shows two circles which intersect at A and B. The center of the smaller circle is O and lies on the circumference of the larger circle. Given ∠APB = a°.
Calculate, in terms of a°, the value of :
(i) obtuse ∠AOB,
(ii) ∠ACB,
(iii) ∠ADB.
Give reasons for your answers clearly.