Question

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


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Answer 1

Answer:

6. 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.

Question 6. 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.

Solution: It is given that line YQ bisects ∠PYZ.

Hence,

∠QYP = ∠ZYQ

PX is straight line

sum of angle in linear pair always equal to 180°

∠XYZ + ∠ZYQ + ∠QYP = 180°

Give that so plug the value we get ∠ XYZ = 64°

And ∠QYP = ∠ZYQ

∠ 64° + 2∠QYP = 180°

∠2∠QYP = 180° − 64° = 116°

Divide by 2 we get

∠QYP = 58°

Also, ∠ZYQ = ∠QYP = 58°

Using angle of reflection

∠QYP = 360° − 58° = 302°

∠XYQ = ∠XYZ + ∠ZYQ

= 64° + 58°

= 122°

Answer 2

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It is given that line YQ bisects ∠PYZ.

Hence,

∠QYP = ∠ZYQ

PX is straight line

sum of angle in linear pair always equal to 180°

∠XYZ + ∠ZYQ + ∠QYP = 180°

Give that so plug the value we get ∠ XYZ = 64°

And ∠QYP = ∠ZYQ

∠ 64° + 2∠QYP = 180°

∠2∠QYP = 180° − 64° = 116°

Divide by 2 we get

∠QYP = 58°

Also, ∠ZYQ = ∠QYP = 58°

Using angle of reflection

∠QYP = 360° − 58° = 302°

∠XYQ = ∠XYZ + ∠ZYQ

= 64° + 58°

= 122°

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