Question 1132329
It is a property of circles and secants that if two secants intersect outside of the circle (PB and PD) the angle formed (angle P) will be 1/2 the difference of the two intercepted arcs:  angle P = 1/2(arc_BD - arc_AC)<br>

Angle Q is 1/2 arc_AC (inscribed angles are 1/2 their central angle) <br>

angle P +  angle Q = (1/2)(arc_AC) + (1/2)(arc_BD - arc_AC) = (1/2)(arc_BD) = (1/2)(80) = 40 degrees<br>

Remember, the angle of an arc is the <em>central</em> angle that it sweeps, none of which are drawn on the Question 4 diagram<br>