Question 4
Answer all ten questions and show detailed solutions. Printed time 60 minutes; each question 4 points. Subcriterion allocations are editorial.
In triangle $ABC$, $AB=BC$. Point $L$ lies on $BC$ and $AL$ bisects $\angle BAC$. If $AL=AC$, find the size of the angle of triangle $ABC$.
In triangle $ABC$, $AB=BC$. Point $L$ lies on $BC$ and $AL$ bisects $\angle BAC$. If $AL=AC$, find the size of the angle of triangle $ABC$.