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It is given that ∠ XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ ZYP, find ∠ XYQ and reflex ∠QYP.

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From figure, 

∠XYZ = 64°             (Given) 

Now, ∠ZYP + ∠XYZ = 180° 

(Linear pair axiom) ⇒

 ∠ZYP + 64° = 180° 

⇒ ∠ZYP = 180° – 64° – 116° 

Also, given that ray YQ bisects ∠ZYP. 

But, ∠ZYP = ∠QYP ∠QYZ = 116° 

Therefore, ∠QYP = 58° and ∠QYZ = 58° 

Also, ∠XYQ = ∠XYZ + ∠QYZ 

⇒ ∠XYQ = 64° + 58° = 122° 

and reflex ∠QYP = 360° – ∠QYP = 360° – 58° = 302° (∵ ∠QYP = 58°) 

Hence, ∠XYQ = 122° and reflex ∠QYP = 302° Ans.

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