hi maths genius please help this problem give best solution.
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you can check the answer in the pic
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Solutions :-
Given :
∠XYZ = 64°
Ray YQ bisects ∠ZYP.
To find :- (i) ∠XYQ
(ii) Reflex ∠ZYP
Find the ∠ZYP :-
∠ZYP + ∠XYZ = 180° [ Linear pair]
=> ∠ZYP + 64° = 180°
=> ∠ZYP = 180° - 64° = 116°
Therefore,
∠ZYP = ∠OYP + ∠QYZ = 116°
∠OYP = ∠QYZ. [ YQ bisects ∠ZYP ]
=> ∠OYP + ∠QYZ = 116°
=> ∠OYP + ∠OYP = 116°
=> 2∠OYP = 116°
=> ∠OYP = 116°/2 = 58°
So,
∠OYP = ∠QYZ = 58°
Find the ∠XYQ :-
∠XYQ = ∠XYZ + ∠QYZ
=> ∠XYQ = 64° + 58° = 122°
NOW,
Find the reflex of ∠QYP :-
Reflex = 360° - ∠QYP
= 360° - 58° = 302°
Hence,
(i) ∠XYQ = 122°
(ii) Reflex ∠QYP = 302°
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