Question

it is given that anglexyz=64° and xy is produced to point p draw a figure from the given information. If ray yq bisects anglezyp,Find anglexyq and reflex angleqyp

Answer 1

Answer:

Let XY be a Line forming 180°

∠XYZ + ∠ZYP = 180°(Linear pair)

Or, 64° + ∠ZYP = 180°

Or, ∠ZYP = 180° - 64° = 116°

Since, YQ bisects ∠ZYP 

So, ∠ZYQ = ∠PYQ = ½ ∠ZYP = 116°/2 = 58°

So, ∠XYQ = ∠XYZ + ∠ZYQ = 64°+ 58° = 122°

Now, reflex ∠QYP = 360° - 58° = 302°

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 ❤