Question

If angle ∠XYZ = 64⁰ 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

Given:

• ∠XYZ = 64°
• YQ bisect ∠ZYP

To Find:

• ∠XYQ
• Reflex ∠QYP

Solution:

XP is a straight line.

$\circ \: {\boxed{\tt\pink{ XYZ + ZYP = 180° }}}$

Putting the value of XYZ = 64°,

$\colon\implies$ 64° + ZYP = 180°

$\colon\implies$ ZYP = 116°

We also know that,

$\circ {\boxed{\boxed{\tt {ZYP = ZYQ + QYP }}}}$

Now, As YQ bisects ZYP,

: ZYQ = QYP

Or,

: ZYP = 2( ZYQ )

$\colon\implies$ ZYQ = QYP = 58°

Again, XYQ = XYZ + ZYQ

By putting the value of XYZ = 64° and ZYQ = 58°,

$\colon\implies$ XYQ = 64° + 58°

$\colon\implies$ XYQ = 122°

Hence,

• The Value of ∠XYQ is 122°

Now,

::- Reflex QYP = 180°+ XYQ

$\bullet \: \: \: {\boxed{\underline{\tt{ Value \ of \ XYQ = 122° }}}}$

So,

$\colon\implies$ QYP = 180° + 122°

$\colon\implies$ QYP = 302°

Hence,

• The Value of ∠QYP is 302°.

Answer 2

Step-by-step explanation:

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°