Question

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

Answer 1

Given : ABCD is a cyclic quadrilateral. If ∠BCD = 100° and ∠ABD = 70°.

 

To find :  ∠ADB.

 

Proof :  

We have,

∠BCD = 100° and ∠ABD = 70°

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

∴∠DAB + ∠BCD = 180°

∠DAB + 100° = 180°

∠DAB = 180° - 100°

∠DAB = 80°

 

In ∆ DAB,  

Since Sum of all angles of a triangle is 180°.

∠ADB + ∠DAB + ∠ABD = 180°

∠ABD + 80° + 70° = 180°

∠ABD + 150° = 180°

∠ABD  = 180° - 150°

∠ABD = 30°

Hence the ∠ABD is 30°.

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

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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 :

ABCD is a cyclic quadrilateral. If ∠BCD = 100° and ∠ABD = 70°.

 

To find :

 ∠ADB.

 

Proof :  

We have,

∠BCD = 100° and ∠ABD = 70°

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

∴∠DAB + ∠BCD = 180°

∠DAB + 100° = 180°

∠DAB = 180° - 100°

∠DAB = 80°

 

In ∆ DAB,  

Since Sum of all angles of a triangle is 180°.

∠ADB + ∠DAB + ∠ABD = 180°

∠ABD + 80° + 70° = 180°

∠ABD + 150° = 180°

∠ABD  = 180° - 150°

∠ABD = 30°

Hence the ∠ABD is 30°.

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