Question

In the inscribed quadrilateral ABCD, the side AB, BC, and CD are congruent. AB and DC meet at a 32 degree angle. Find the measure of the angles of ABCD?

AB and DC are secants.

Answer 1

In the inscribed quadrilateral ABCD, the side AB, BC, and CD are

congruent. AB and DC meet at X and `angleBXC =32^@`

As `AB~=BC~=CD`, we have `angleABC=angleBCD`

So in `DeltaBXC` , `angleXBC=angleXCBandangleBXC=32^@`

So

`angleXBC=angleXCBandangleBX=1/2(180^@-32^@)=74^@`

Hence

`angleABC=angleBCD=(180^@-74^@)=106^@`

So`angleCDA=angleDAB=(180^@-106^@)=74^@`