[ Properties and characteristics of an isosceles triangle.] [Sum of the angles of a triangle. Theorem of the exterior angle.]

Triangle $A B C$ is isosceles $(A B=B C)$. Segment $A M$ divides it into two isosceles triangles with bases $A B$ and $M C$. Find angle $B$.
Use the theorems about the exterior angle of a triangle and the sum of the angles of a triangle.

## Solution

Let $\angle B=\beta$. Then $\angle B A M=\beta, \angle A M C=2 \beta, \angle A=\angle C=2 \beta$. Therefore, $\beta+2 \beta+2 \beta=180^{\circ}$, which means $\beta=36^{\circ}$.

## Answer

$36^{\circ}$.