Math, asked by nareshnbjk9846, 10 months ago

If O is the centre of the circle, find the value of x in each of the following figures :

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Answers

Answered by nikitasingh79

Given: O is the center of the circle.

To find : The value of x .

Solution :

(i) From figure : ∠AOC = 135° , ∠COB = x

∴ ∠AOC + ∠BOC = 180°

[Linear pair]

135° + ∠BOC = 180°

∠BOC = 45°

Since, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

∴ ∠BOC = 2 ∠COB

45° = 2x

x = 45°/2

x = 22½°

Hence x is 22½° .

(ii) From figure : ∠ABC = 40° , ∠CDB = x

We know that angle in semi-circle is 90°.

∠ACB = 90°

In ∆ ABC,

Since Sum of the angles of a triangle is 180° :

∴ ∠CAB + ∠ACB + ∠ABC = 180°

∠CAB + 90° + 40° = 180°

∠CAB + 130° = 180°

∠CAB = 180° - 130°

∠CAB = 50°

Now,

Since angles in the same segment of a circle are equal :

∴ ∠CDB = ∠CAB

x = 50°

Hence x is 50°.

(iii) From figure : ∠AOC = 120° , ∠CBD = x

Since, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

∠AOC = 2 ∠APC

120° = 2 ∠APC

∠APC = 120°/2

∠APC = 60°

Since, APCB is a cyclic quadrilateral, and Sum of Opposite pair of angles in a cyclic quadrilateral is 180° :

∴ ∠APC + ∠ABC = 180°

60° + ∠ABC = 180°

∠ABC = 180° - 60°

∠ABC = 120°

∠ABC + ∠DBC = 180°

[Linear pair]

120° + x = 180°

x = 180° - 120°

x = 60°

Hence x is 60°.

HOPE THIS ANSWER WILL HELP YOU…..

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In Fig. 16.120, O is the centre of the circle. If ∠APB=50°, find ∠AOB and ∠OAB.

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In Fig. 16.122, O is the centre of the circle. Find ∠BAC.

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Answered by Anonymous

Answer:From figure : ∠AOC = 135° , ∠COB = x