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Question Number 6806 by Tawakalitu. last updated on 27/Jul/16

	Answered by Yozzii last updated on 28/Jul/16

	$W e h a v e t h a t ∠ Q S R = 40 ° . L e t ω b e$ $c i r c l e P Q R S . P o i n t s S a n d P l i e o n$ $ω o n t h e s a m e s i d e o f l i n e Q R .$ $\Rightarrow ∠ Q S R = ∠ Q P R ∴ ∠ Q P R = 40 ° .$ $T U i s a s t r a i g h t l i n e, s o$ $∠ T P S + ∠ S P R + ∠ Q P R = 180 °$ $\Rightarrow ∠ S P R = 180 ° - 40 ° - 74 ° = 66 °$ $A n g l e s ∠ S P R a n d ∠ S Q R a r e i n t h e$ $s a m e s e g m e n t o f ω \Rightarrow ∠ S Q R = ∠ S P R = 66 ° .$ $W e k n o w t h a t ∠ R Q U = 68 °$ $N o w, ∠ P Q S + ∠ S Q R + ∠ R Q U = 180 °$ $\Rightarrow ∠ P Q S = 180 ° - 66 ° - 68 ° = 46 ° .$ $S i n c e ∠ P Q S a n d ∠ P R S l i e i n t h e m a j o r$ $s e g e m e n t P Q R S, ∠ P R S = ∠ P Q S = 46 ° .$
	Commented by Tawakalitu. last updated on 28/Jul/16

	$W o w t h a n k s .$
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