If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio $2:3,$ then the greater of the two angles is (in $^{\circ}$)

In the given figure,if $PQ || RS$,$RS || MN$ and $y: z = 7: 11$,then find $x$. (in $^o$)

In $\Delta ABC$,the sides $AB$ and $AC$ are produced to $D$ and $E$ respectively,so that exterior angles $\angle CBD$ and $\angle BCE$ are formed. If bisectors of $\angle CBD$ and $\angle BCE$ intersect at point $O$,prove that $\angle BOC = 90^{\circ} - \frac{1}{2} \angle A$.

The sum of the three angles of a triangle is $\ldots \ldots \ldots$ (in $^o$)

$\angle ABD$ and $\angle DBC$ are adjacent angles. If $\angle ABD = 1.5x^{\circ}$,$\angle DBC = 2x^{\circ}$,and $\angle ABC = 70^{\circ}$,then find $x$ and the measures of $\angle ABD$ and $\angle DBC$.

$\angle ACD$ is an exterior angle of $\Delta ABC$. If $\angle A = 70^{\circ}$ and $\angle B = 40^{\circ}$ in $\Delta ABC$,then find $\angle ACD$. (in $^{\circ}$)