Question

In Fig. 16.188, ABCD is a cyclic quadrilateral. Find the value of x.

Answer 1

Given : ABCD is a cyclic quadrilateral.

 

To find :  The value of x.

 

Proof :  

From figure we have,  

∠FDC = 80° and ∠ABE = x°

∠FDC + ∠CDA = 180° (Linear pair)

80° + ∠CDA = 180°

∠CDA = 180° - 80°

∠CDA = 100°

 

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

∠CDA + ∠ABC = 180°

100° + ∠ABC = 180°

∠ABC = 180° - 100°

∠ABC = 80°  

Now,

∠ABC + ∠ABE = 180° (Linear pair)

80° + x = 180°

x = 180° - 80°

x = 100°

Hence the value of x is 100° .

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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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Answer 2

Answer:-

Given :

ABCD is a cyclic quadrilateral.

 

To find :

 The value of x.

 

Proof :  

From figure we have,  

∠FDC = 80° and ∠ABE = x°

∠FDC + ∠CDA = 180° (Linear pair)

80° + ∠CDA = 180°

∠CDA = 180° - 80°

∠CDA = 100°

 

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

∠CDA + ∠ABC = 180°

100° + ∠ABC = 180°

∠ABC = 180° - 100°

∠ABC = 80°  

Now,

∠ABC + ∠ABE = 180° (Linear pair)

80° + x = 180°

x = 180° - 80°

x = 100°

Hence the value of x is 100° .

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