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.

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Answer 1

Answer:-

• ∠XYQ = 122°
• ∠QYP = 302°

Given:-

• ∠XYZ = 64°
• YQ bisects ∠ZYP

To Find:-

• ∠XYQ
• Reflex ∠QYP.

Solution:-

XY is produced to point P.

According to the question,

⇒ ∠XYZ +∠ZYP = 180° (Linear Pair)

⇒ 64° +∠ZYP = 180°

⇒ ∠ZYP = 116°

also,

⇒ ∠ZYP = ∠ZYQ + ∠QYP

⇒ ∠ZYQ = ∠QYP (YQ bisects ∠ZYP)

⇒ ∠ZYP = 2∠ZYQ

⇒ 2∠ZYQ = 116°

⇒ ∠ZYQ = 58° = ∠QYP

Now,

∠XYQ = ∠XYZ + ∠ZYQ

⇒ ∠XYQ = 64° + 58°

⇒ ∠XYQ = 122°

also reflex,

⇒ ∠QYP = 180° + ∠XYQ

⇒ ∠QYP = 180° + 122°

⇒ ∠QYP = 302°

Hence,

• ∠XYQ = 122°
• ∠QYP = 302°

Answer 2

Answer:

Here, XP is a straight line

So, ∠XYZ +∠ZYP = 180°

substituting the value of ∠XYZ = 64° we get,

64° +∠ZYP = 180°

∴ ∠ZYP = 116°

From the diagram, we also know that ∠ZYP = ∠ZYQ + ∠QYP

Now, as YQ bisects ∠ZYP,

∠ZYQ = ∠QYP

Or, ∠ZYP = 2∠ZYQ

∴ ∠ZYQ = ∠QYP = 58°

Again, ∠XYQ = ∠XYZ + ∠ZYQ

By substituting the value of ∠XYZ = 64° and ∠ZYQ = 58° we get.

∠XYQ = 64° + 58°

Or, ∠XYQ = 122°

Now, reflex ∠QYP = 180° + ∠XYQ

We computed that the value of ∠XYQ = 122°. So,

∠QYP = 180° + 122°

∴ ∠QYP = 302°