Question

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


100° , 200°

122° , 302°

29° , 58°

Option 4

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Answer 1

Answer:

so watch this carefully.........

Step-by-step explanation:

angle XYZ+ angle ZYP= 180° (linear pair )

Therefore angle XYQ = 180° - angle XYZ

= 180-64

=116°

Angle XYQ = 116°

Now , reflex of angle QYP

(bisect means divide angle to equal parts.)

116°/2

58°

so, reflex = (180+64+58) or 360°-58°

= 302°

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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 :-

i.e : 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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