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 1

REFER TO THE IMAGE FOR FIGURE

it is given that,

∠ XYZ = 64°

since, XYP is a line therefore,

∠ XYZ + ∠ ZYQ + ∠QYP = 180°

(it is given that YQ is the bisector of ∠ ZYP so,

∠ ZYQ = ∠ PYQ   SO WE WILL GET, )

64° + 2 ∠ ZYQ = 180°

2 ∠ ZYQ = 180° - 64°

∠ ZYQ = 58° = ∠ PYQ

SO,

∠ XYQ = ∠ XYZ + ∠ ZYQ

∠ XYQ = 64° + 58 °

∠ XYQ = 122°

ref ∠ QYP = 360° - ∠ QYP

ref ∠ QYP = 360° - 58°

ref ∠ QYP = 302°

Answer 2

Solution:

Here,

XP is a straight line

So, XYZ +ZYP = 180°

Putting the value of XYZ = 64° we get,

64° +ZYP = 180°

∴ ZYP = 116°

From the diagram, we also know that ZYP = ZYQ + QYP

Now, as YQ bisects ZYP,

ZYQ = QYP

Or, ZYP = 2ZYQ

∴ ZYQ = QYP = 58°

Again, XYQ = XYZ + ZYQ

By putting the value of XYZ = 64° and ZYQ = 58° we get.

XYQ = 64°+58°

Or, XYQ = 122°

Now, reflex QYP = 180°+XYQ

We computed that the value of XYQ = 122°.

So,

QYP = 180°+122°

∴ QYP = 302°