Question

if one side of a cyclic quadrilateral is produced then exterior angle is equal to interior opposite angle ​

Answer 1

Answer:

yes the exterior angle made by producing any of side of a cyclic quadrilateral is equal to the angle opposite to the interior angle made by the corresponding sides.

Step-by-step explanation:

Answer 2

AnswEr:

$\star$$\bf\underline{Given:}$

A cyclic quadilateral ABCD one of whose side AB is produced to E.

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$\star$$\bf\underline{To\:prove:}$

$\angle$$\sf{CBE=\angle\:ADC}$

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$\star$$\bf\underline{Proof:}$

Since ABCD is a cyclic quadilateral and the sum of opposite pairs of angles in a cyclic quadilateral is 180°.

$\therefore$$\sf\qquad{\angle\:ABC+\angle\:ADC=180°}$

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But, $\sf{\angle\:ABC+\angle\:CBE=180°}$$\sf\qquad{[linear\:pair]}$

$\therefore$ $\sf{\angle\:ABC+\angle\:ADC=\angle\:ABC+\angle\:CBE}$

$\rightarrow$$\sf{\angle\:ADC=\angle\:CBE}$

or, $\sf{\angle\:CBE=\angle\:ADC}$

#BAL

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