A line passing through vertex $A$ of triangle $ABC$ intersects side $BC$ at point $M$. In this case, $BM = AB$, $\angle BAM = 35^\circ$, and $\angle CAM = 15^\circ$.

Find the angles of triangle $ABC$.
Use the theorem about the sum of the angles of a triangle.

## Answer

$50^{\circ}, 110^{\circ}, 20^{\circ}$.

A line passing through vertex $A$ of triangle $ABC$ intersects side $BC$ at point $M$, and $BM = AB$.

Find the difference between angles $BAM$ and $CAM$ if $\angle C = 25^{\circ}$.

## Hint

$\angle B A M = \angle B M A = \angle M A C + \angle M C A$.

## Solution

Since triangle $ABM$ is isosceles, $\angle B A M = \angle B M A$, and since $BMA$ is the exterior angle of triangle $AMC$, then $\angle B M A - \angle M A C = \angle A C B = 25^{\circ}$.

## Answer

$25^{\circ}$.