Why this type of triangle has more properties?

$2\alpha+ 2\beta = 180^\circ \implies \angle A = \alpha + \beta = 90^\circ$

SOLUTION WITHOUT WORDS

Let the angle made by $PA$ with $AB$ and $AC$ be $\alpha$ and $\beta$ respectively.

Now, the fact that angle of incidence and angle of reflection are same shows that the following hold : $\angle PAQ = 2\alpha \\ \angle PAR = 2\beta$

As $QAR$ is a straight line, $\angle PAQ + \angle PAR = 180^\circ \implies \angle A = \alpha + \beta = 90^\circ$