Question

A $△ABC$ is right angled at $A.L$ is a point on $BC$ such that $AL\perp BC$ that $\angle BAL=\angle ACB$

Answer 1

$\Delta ABC$

By angle sum property

$\angle ABC+\angle ACB+\angle BAC=180\angle ABC+\angle ACB=180-90=90\cdots \left(1\right)$

$\Delta ABL$

By angle sum property

$\angle ABL+\angle ALB+\angle BAL=180\angle ABL+\angle BAL=180-90=90\cdots \left(2\right)$

$\angle ABC+\angle ACB=\angle ABL+\angle BAL$

$\angle ABC=\angle ABL⟹\angle BAL=\angle ACB$