Finding the Measure of Angle LSM in a Right-Angled Triangle with an Inscribed Circle

Question

In a right-angled triangle KLM with a right angle at the vertex K, S is the center of the circle inscribed in it. The size of the LSM angle is:

The answer is 135º but I don't where to start, or how to do this question.

Answer 1

A line drawn from a vertex to the center of an incircle bisects the angle at that vertex, and the internal angles of a triangle must add up to 180˚. In the diagram below, \begin{align*} \,2\alpha+2\beta=90˚\\ \implies\alpha + \beta=45˚\\ \implies \gamma=180˚-45˚=135˚ \end{align*}