Question

It is given XYZ=64 and XY is produced to point P.Aray YQ bisects ZYP. Draw a figure from the given information. Find XYQ and reflex QYP
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Answer 1

given √XYZ =64°

now,√xyz +√zyp =180°

or 64°+√zyp =180°

or √zyp= 180°- 64° = 116°

since yQ. bisects √zyp

so,√zyQ = √pyQ = 1/2 √zyp = 116°/2= 580°

so,√xyQ = √xyz +√zyQ = 64°+ 58° = 122°

now reflex √Qyp = 360° - 58° = 302° answer....

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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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