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°.