Question

6. It is given that angle XYZ=64° and XY is produced
to point P. Draw a figure from the given
information. If ray YQ bisects angle ZYP, find angle XYQ
and reflex angle QYP.​

Answer 1

Answer:

$\boxed{ \large\mathtt{answer: \angle{QYP} = 302 \degree}}$

#Given,

∠XYZ=64∘

YQ bisects ∠ZYP

∠XYZ + ∠ZYP = 180∘ (Linear Pair)

64∘ + ∠ZYP = 180∘

∠ZYP = 180° – 64°

∠ZYP = 116∘

#Also, ∠ZYP = ∠ZYQ + ∠QYP

∠ZYQ = ∠QYP (YQbisects∠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∘

• ᴍʀᴋ. ᴛʜᴀɴᴋs ᴀɴᴅ ʙʀᴀɪɴʟɪsᴛ

Answer 2

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 :-

ie : XYP is a straight line.

∴ ∠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° = 116°

⇒ ∠QYP = 116°/2 = 58°

∴ Reflex ∠QYP = 360° – 58° = 302°

Since ∠XYQ = ∠XYZ + ∠ZYQ

⇒ ∠XYQ = 64° + ∠QYP [∵∠XYZ = 64°(Given) and ∠ZYQ = ∠QYP]

⇒ ∠XYQ = 64° + 58° = 122° [∠QYP = 58°]

Thus, ∠XYQ = 122° and reflex ∠QYP = 302°.

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