Question

If the internal opposite angle is 51 degree then find the external angle of a cyclic quadrilateral

Answer 1

Step-by-step explanation:

Given Data

Internal opposite angle a Quadrilateral is 51°

To find - the external angle of a Quadrilateral

Consider a cyclic Quadrilateral with ABCD

Internal opposite of the cyclic Quadrilateral is ∠ADC

where, ∠ADC = 51°

External opposite angle of the Quadrilateral is ∠CBE

In a cyclic Quadrilateral opposite angles are supplementary

∠ABC + ∠ADC = 180° ----------------> 1

∠ABC and ∠CBE are linear pair angles which is also equals to 180°

∠ABC + ∠CBE = 180° -----------------> 2

On equate 1 and 2 we get

∠ABC + ∠ADC = ∠ABC + ∠CBE

Eliminate ∠ABC on both sides we get

∠ADC = ∠CBE

∠ADC = 51° then , ∠CBE = 51°

where ∠CBE is the external angle of a cyclic Quadrilateral

The external angle of a cyclic Quadrilateral is 51° and also it is proved that the internal opposite angle is equals to the external opposite angle of a cyclic Quadrilateral.