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

Answer:

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°

Answer 2

Answer:

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*