Question

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

Answer 1

Answer:

AB=CD

B=70

D=70

A+70=180

A=180-70

A=110

C=110

Answer 2

Given : In a cyclic quadrilateral ABCD if AB || CD and B = 70°.

 

To find :  The remaining angles.

 

Proof :  

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

∴ ∠B + ∠D = 180°

70° + ∠D = 180°

∠D = 180° - 70°

∠D = 110°

 

Since, AB ‖ DC and BC is a transversal and sum of the interior angles on the same side of a transversal is 180°.

∴ ∠B + ∠C = 180°

70° + ∠C = 180°

∠C = 180° - 70°

∠C = 110°

 

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

∠A + ∠C =180°

∠A +  110° = 180°

∠A = 70°

Hence , the  remaining angles be ∠A = 70°, ∠C = 110°  and ∠D = 110°.

HOPE THIS ANSWER WILL HELP YOU…..

 

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