In a cyclic quadrilateral `A B C D`, if `AB` `|\|` `CD\ a n d\ /_B=70^@,` find the remaining angles.

Explanation

Given `ABCD` is a cyclic quadrilateral
and also `AB |\| CD`
As `AB|\|CD`, and `BC` is the transversal
So `/_B+/_C=180^@`
`=>/_C=180 ^@ −70^@ =110^@`
In a cyclic quadrilateral ,Sum of opposite angles will be `180^@`
`=>/_A+/_C=180^@and∠B+/_D=180^@`
`=>/_A=180^@−/_C=180 ^@−110^@=70^@` and
`/_D=180^@ −/_B=180^@ −70^@=110 ^@`
So the remaining angles are `/_A=70^@ ,/_C=110 ^@,/_D=110^@`