Prove that in a cyclic quadrilateral opposite angle are supplementary.
WBBSE
Class X
Mathematics
Theorems Related To Cyclic Quadrilateral
05 Mark
2023
Given: ABCD is a cyclic quadrilateral
To prove: ∠ABC + ∠ADC = 2 right angles and ∠BAD + ∠BCD = 2 right angles
Construction: Two diagonals AC and BD are drawn.
Proof: ∠ADB = ∠ACB [angles in the same segment of the circle]
Again, ∠BAC = ∠BDC [angles in the same segment of the circle]
Again, ∠ADC = ∠ADB + ∠BDC
= ∠ACB + ∠BAC
∴ ∠ADC + ∠ABC = ∠ACB + ∠BAC + ∠ABC
∴ ∠ADC + ∠ABC = 2 right angles [∴ sum of three angles of a triangle is 2 right angles]
Similarly we can prove that, ∠BAD + ∠BCD = 2 right angles
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