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Theorem : Opposite Angles of a Cyclic Quadrilateral are Supplementary | Class 8

Theorem : Opposite Angles of a Cyclic Quadrilateral are Supplementary.

Solution :

Given: ABCD is a cyclic quadrilateral.
R.T.P.(Require To Prove)

1.BAD + BCD = 1800
     2.ABC + ADC = 1800

Construction : Join OB and OD
Proof:

1.  BOD = 2 ∠BAD || Angle at the centre of a circle is twice the angle at the circumference.
2.  Reflex BOD + BOD = 2 (BAD + BCD) || Same as stated above.
  or   2 (BAD + BCD) = 3600 || By statement 2.
or   (BAD + BCD) = 1800
3. Similarly by joining OA and OC it can be proved that
  ABC + ADC = 1800
4.   BAD + BCD = 1800
&      ABC + ADC = 1800   Proved

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