Question

5. 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 angleZYP, find angle XYQ
and reflex angleQYP.​

Answer 1

Answer :

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°

∠ 64° + 2∠QYP = 180°∠2∠QYP = 180° − 64° = 116°

Divide by 2 we get

Divide by 2 we get∠QYP = 58°

Also,

∠ZYQ = ∠QYP = 58°

Using angle of reflection

∠QYP = 360° − 58° = 302°

∠QYP = 360° − 58° = 302°∠XYQ = ∠XYZ + ∠ZYQ

= 64° + 58°

= 122°

Hope it helps☺

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°.

Plz mrk as brainliest ❤