The vertical angle of an isosceles triangle is $100°.$ Find its base angles.

In the given figure, $AB=AC,$ $\angle ACD=105°$. Find $\angle BAC$.

In the given figure, $AB=AC$ and $DB=DC$, find $\angle ABD:\angle ACD$.

Determine the measure of each of the equal angles of a right-angled isosceles triangle.

or

$ABC$ is a right-angled triangle in which $\angle A=90°$ and $AB=AC$. Find $\angle B$ and $\angle C$.

In the given figure, $PQRS$ is a square and $SRT$ is an equilateral triangle. Prove that$PT=QT$.

In the given figure, $PQRS$ is a square and $SRT$ is an equilateral triangle. Prove that $\angle TQR=15°$.

$AB$ is a line segment.$P$ and $Q$ are points on opposite sides of$AB$ such that each of them is equidistant from the points $A$ and $B$ (See figure). Show that the line $PQ$ is the perpendicular bisector of $AB.$