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✤ Required Proof:

✒ GiveN:

• A cyclic quadrilateral.

✒ To prove:

• Outer angle of a cyclic quadrilateral is equal to the inner angle at opposite VERTEX !!

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✤ How to Solve?

For PROVING the above statement, we need to KNOW a theoram based on Cyclic quadrilaterals( The quadrilateral inside a circle, whose vertices touched the circumference)

➤ The sum of opposite angles in a cyclic quadrilateral is supplementary i.e. they add UPTO 180°

So, Let's use this theoram, to prove this statement.

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✤ Solution:

✒ Refer to the attachment.....

According to theoram,

⇛ ∠CBA + ∠CDA = 180°...........(1)

[ Sum of opposite angles = 180°]

Now in line AE,

⇛ ∠CBA + ∠CBE = 180°...........(2)

[ These angles add upto 180° as they form a straight line, hence they are linear pair.]

From equation, (1) and (2)

⇛ ∠CBA + ∠CDA = ∠CBA + ∠CBE

⇛∠CDA = ∠CBE ( ∠CBA cancels both sides)

Here,

• ∠CDA = Angle at opposite to ∠CBA
• ∠CBE = Outer/Exterior angle of ∠CBA

✒ And, We proved that both of these angles are equal, Hence, Proved !

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