$\angle ABD$ and $\angle ACE$ are exterior angles of $\Delta ABC$. If $\angle ABD = 140^{\circ}$ and $\angle ACE = 80^{\circ}$,then find $\angle A$. (in $^{\circ}$)

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 $\angle BOC = 90^{\circ} - \frac{1}{2} \angle A$.

$\angle ABD$ 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 $\Delta ABC$. The bisector of $\angle ABC$ and exterior $\angle ACD$ intersect each other at point $E$. Prove that,$\angle BEC = \frac{1}{2} \angle BAC$.

If two parallel lines are intersected by a transversal,then interior angles on the same side of the transversal are $\ldots \ldots . . .$

Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.