Question

It is given that ∠XYZ = 60°
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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Answer 1

It is given that ∠XYZ = 60°

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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Answer 2

Given:

• ∠XYZ = 60°
• XY is produced to point P.

To Find:

• ∠XYQ and reflex ∠QYP.

Solution:

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 = 180º

⇒ 64º + 2∠QYP = 180º

⇒ 2∠QYP = 180º − 64º = 116º

⇒ ∠QYP = 58º

Also

• ∠ZYQ = ∠QYP = 58º

Reflex ∠QYP

= 360º − 58º

= 302º

→ ∠XYQ = ∠XYZ + ∠ZYQ

→ 64º + 58º = 122º

→ ∠XYQ = 122°

Hence,

• ∠XYQ = 122°
• ∠QYP = 302°