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प्रश्न
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.
उत्तर
It is given that line YQ bisects ∠PYZ.
Hence, ∠QYP = ∠ZYQ
It can be observed that PX is a line. Rays YQ and YZ stand on it.
∴ ∠XYZ + ∠ZYQ + ∠QYP = 180°
64° + ∠ZYQ + ∠QYP = 180° ...[∵ ∠XYZ = 64° (given)]
⇒ 64° + 2∠QYP = 180° ...[YQ bisects ∠ZYP so, ∠QYP = ∠ZYQ]
⇒ 2∠QYP = 180° − 64°
⇒ 2∠QYP = 116°
⇒ ∠QYP = `(116°)/2`
⇒ ∠QYP = 58°
Also, ∠ZYQ = ∠QYP = 58°
Reflex ∠QYP = 360° − 58°
∠QYP = 302°
Since, ∠XYQ = ∠XYZ + ∠ZYQ
⇒ ∠XYQ = 64° + ∠QYP ...[∵ ∠XYZ = 64° (Given) and ∠ZYQ = ∠QYP]
⇒ ∠XYQ = 64° + 58° ...[∠QYP = 58°]
⇒ ∠XYQ = 122°
Thus, ∠XYQ = 122° and reflex ∠QYP = 302°.
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