One of the base angles of an isosceles triangle is $52°.$ Find its angle of vertex.

In the given figure, $\text{BI}$ is the bisector of $\angle ABC$ and $\text{CI}$ is the bisector of $\angle ACB$. Find $\angle \text{BIC.}$

In the given figure, express $a$ in terms of $b.$

In figure (i) $BP$ bisects $\angle ABC$ and $AB=AC$. Find $x.$