Question

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

Answer 1

Answer:

hellow

given -

1. ZXY = 64°
2. produced to point P.
3. YQ bisects ZYP

To find -

1. ZZYP
2. reflex ZQYP

To proof -

we all know that sum on straight line is is 180°

so, angle 1 + 2 + 64 = 180°

1 + 1 + 64 = 180°. (YQ bisects ZYP .so, 1=2)

2 angle 1+64=180°

1 = 180°-64/2

1= 58

so,

2= 58 (ZYP)

reflex ZQYP =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 ❤