Question

In Fig. 16.183, O is the centre of the circle ∠DAB=50°. Calculate the values of x and y.

Answer 1

Given : O is the centre of the circle ∠DAB = 50°

 

To find :  The values of x and y.

 

Proof :  

We have : ∠DAB = 50°

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. :

∴ ∠BOD = 2 ∠DAB

x = 2 × 50°  

x = 100°

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

∴ ∠A + ∠C = 180°

50° + y = 180°

y = 180° - 50°

y = 130°

Hence the value of x is 100° and y is 130°.

HOPE THIS ANSWER WILL HELP YOU…..

 

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In Fig. 16.179 ABCD is a cyclic quadrilateral. If ∠BCD=100° and ∠ABD=70°, find ∠ADB.

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In a cyclic quadrilateral ABCD if AB||CD and B=70°, find the remaining angles.

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Answer 2

Answer:-

Given :

O is the centre of the circle ∠DAB = 50°

 

To find :  

values of x and y.

 

Proof :  

We have : ∠DAB = 50°

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. :

∴ ∠BOD = 2 ∠DAB

x = 2 × 50°  

x = 100°

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

∴ ∠A + ∠C = 180°

50° + y = 180°

y = 180° - 50°

y = 130°

Hence the value of x is 100° and y is 130°.

Hope it's help You❤️