Solution:
![\[ABCD\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-be7837607d267032f3849f5aa4f30674_l3.png "Rendered by QuickLaTeX.com")
is a cyclic quadrilateral,
![\[\angle BCD\text{ }+~\angle BAD\text{ }=\text{ }{{180}^{\circ }}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b60064a693160090bcbc3afd97189b6b_l3.png "Rendered by QuickLaTeX.com")
[Opposite angles of a cyclic quadrilateral are supplementary]
![\[\angle BCD\text{ }+\text{ }{{70}^{o}}~=\text{ }{{180}^{\circ }}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-46aca3f53763bb13fa5606d227de743d_l3.png "Rendered by QuickLaTeX.com")
![\[\angle BCD\text{ }=\text{ }{{180}^{o}}~\text{ }{{70}^{o}}~=\text{ }{{110}^{o}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b185075858363b2bba7665cc2e4b148d_l3.png "Rendered by QuickLaTeX.com")
And, by angle sum property of
![\[\vartriangle BCD\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-14ace5071332ce59842f2387fece03b7_l3.png "Rendered by QuickLaTeX.com")
we have
![\[\angle CBD\text{ }+~\angle BCD\text{ }+~\angle BDC\text{ }=\text{ }{{180}^{o}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8e676269ab2182074db45b157051941a_l3.png "Rendered by QuickLaTeX.com")
![\[{{30}^{o}}~+\text{ }{{110}^{o}}~+~\angle BDC\text{ }=\text{ }{{180}^{o}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4197a65fd752829bce35a888ead8dfce_l3.png "Rendered by QuickLaTeX.com")
Or,
![\[\angle BDC\text{ }=\text{ }{{180}^{o~}}-\text{ }{{140}^{o}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9aab07b8e10097662cf7522f78222aa5_l3.png "Rendered by QuickLaTeX.com")
Thus,
![\[\angle BDC\text{ }=\text{ }{{40}^{o}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ed6cfc4c0c9e2aaa7cafd598c2441715_l3.png "Rendered by QuickLaTeX.com")
Solution:
is a cyclic quadrilateral,
[Opposite angles of a cyclic quadrilateral are supplementary]
And, by angle sum property of
we have
Or,
Thus,
