Question 1163164
<pre>
{{{

drawing(400,800/3,-1,11,-1,7,
locate(0,0,B), locate(10,0,C), locate(4.9,6.4,A),
locate(6,5.25,Q),locate(3.8,5.25,R),locate(4.9,4,P),

triangle(0,0,10,0,5,5.958767963), green(line(5.868240888,4.924038765,0,0)),
red(line(4.131759112,4.924038765,10,0)) )}}}

The drawing is to scale.

Since you are given angle BPC, you also know angle RPQ. 
You are also given angles ARP and AQP, if you know what the word
"perpendicular" means.

The sum on the 4 interior angles of any quadrilateral must have sum 360°.
You know the sum of the angles of quadrilateral ARPQ, so you can easily
determine angle A.

Edwin</pre>