Question

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.

Answer 1

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°.