Is my work correct? Given: ABCD is an inscribed polygon.Prove: ∠A and​ ∠C ​ are supplementary angles.

Solution:Given: A B CD is an inscribed polygon.To Prove: ∠A and​ ∠C ​ are supplementary angles.Proof: Join AC and B D.Angle in the same segment of a circle are equal. ∠ACB=∠ADB→→AB is a segment.Also, ∠A B D=∠A CD→→AD is a Segment.In Δ ABD∠A+∠ABD+∠ADB=180°→→Angle sum property of triangle.∠A+∠A CD+ ∠ACB=180°∠A+∠C=180°Hence proved, that is, ∠A and​ ∠C ​ are supplementary angles.The method Adopted by you∠1=2 ∠A----(1)and, ∠2=2 ∠C-------(2)The theorem which has been used to prove 1 and 2, Angle subtended by an arc at the center is twice the angle subtended by it any point on the circle.→(Inscribed angle theorem)Also, angle in a complete circle measures 360°.→→Chord arc theorem∠1+∠2=360°→→Addition Property of Equality2∠A+2∠C=360°→→[Using 1 and 2, Called Substitution Property]Dividing both sides by 2→→Division Property of Equality2∠A+2∠C=360°→→[Using 1 and 2]∠A+∠C=180°→→Correct work.