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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 ∠XYO and reflex ∠QYP.

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Data: ∠XYZ = 64° and XY is produced upto P. 

∠ZYP is bisected. 

To Prove: ∠XYQ = ? 

Reflex ∠QYP = ? 

Proof: YQ bisects ∠ZYP 

∴ Let ∠PYQ = ∠ZYQ = x°. 

∠XYZ + ∠ZYQ + ∠QYP = 180° 

(∵ ∠XYP is straight angle) 

64 + x + x = 180 

∴ 64 + 2x = 180 

∴ 2x= 180 – 64 

2x = 116 

∴ x = \(\frac{116}{2}\) = 58°

∴ ∠PYQ = ∠ZYQ = 58°

(i) ∴ ∠XYQ= ∠XYZ + ∠ZYQ = 64 + 58 

∠XYQ= 122° 

(ii) Reflex ∠QYP = ∠PYX + ∠XYZ + ∠ZYQ 

= 180 ° + 64° + 58° 

= 180+122 

∴ Reflex ∠QYP = 302°.

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