Circle Geometry Question (1 Viewer)

[Heresy]

I'm having trouble with this question (and pretty much the rest of Circle Geometry).
Any tips?

 

[quickoats]

(i)
<PRQ= ½α (angle subtended by an arc at the centre of the circle is twice the angle at the circumference subtended by the same arc)
<QRM=180°=pi (straight line)
because <PRQ+<PRM=pi
<PRM=pi-½α
(ii)
similarly, <QSM=pi-½α (same proof as part (i))
<SNR=<PNQ (vertically opposite angles)
<SNR+<QSM+<PMQ+<PRM=360° (angle sum of a quadrilateral)
from the previous steps we can substitute values
<PNQ+<PMQ+180°-½α+180°-½α=360°
<PNQ+<PMQ-α=0
Hence, <PNQ+<PMQ=α

 

[Heresy]

(i)
<PRQ= ½α (angle subtended by an arc at the centre of the circle is twice the angle at the circumference subtended by the same arc)
<QRM=180°=pi (straight line)
because <PRQ+<PRM=pi
<PRM=pi-½α
(ii)
similarly, <QSM=pi-½α (same proof as part (i))
<SNR=<PNQ (vertically opposite angles)
<SNR+<QSM+<PMQ+<PRM=360° (angle sum of a quadrilateral)
from the previous steps we can substitute values
<PNQ+<PMQ+180°-½α+180°-½α=360°
<PNQ+<PMQ-α=0
Hence, <PNQ+<PMQ=α

Thank you so much!