Solution :
Proof:
Given: ABCD is a cyclic quadrilateral.
R.T.P.(Require To Prove)
1. ∠BAD + ∠BCD = 1800
2. ∠ABC + ∠ADC = 1800
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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