Question

It is given that angle XYZ=64° and XY is produced to point P. Draw a figure from the given information. if ray YQ bisects angle ZYP, find angle XYQ and reflex angle QYP

Answer 1

<XYQ value is 122°, and <QYP is 302°

Given,

<XYZ = 64°.

To Find,

The value of <XYQ

Solution,

Given that the <XYZ = 64°

and <ZYP is bisect by the YQ line.

Angle XYZ and ZYP are liner pair, so its sum will be,

<XYZ + <ZYP = 180°

<XYZ = 64°

<ZYP = 180 - 64

<ZYP = 116°.

Also from the figure it is clear that,

<ZYP = < ZYQ + <QYP

And YQ bisect <ZYP,

Angle ZYQ and QYP are the same.

<ZYP = 2<ZYQ

<ZYP = 116°

2<ZYQ  =  116°

<ZYQ = $\frac{116}{2}$

<ZYQ = 58°.

<ZYQ and <QYP is equal to 58°

We need to find the value of angle XYQ,

from figure,

<XYQ = <XYZ + <ZYQ

<XYZ = 64° and <ZYQ = 58°.

Therefore, the value of angle XYQ,

<XYQ = 64 + 58

<XYQ = 122°.

Need to reflex the angle QYP,

<QYP  = 180 + <XYQ

<QYP = 180 + 122

<QYP = 302°

Hence, 122° is the value of angle XYQ.

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Answer 2

Answer:

The correct answer is $\angle QYP = 302^{0}$ and $\angle XYQ = 122^{0} .$

Step-by-step explanation:

Given:

$\angle XYZ = 64^{0}$

To find:

• The angle $XYQ$ and reflex angle $QYP$
• Draw a figure from the given information.

Step 1

$XYP$ is a straight line,

$\angle X Y Z+\angle Z Y P=180^{\circ} \quad$ (Linear pair)

$\angle Z Y P=180^{\circ}-\angle X Y Z$

$\angle Z Y P=180^{\circ}-64^{\circ}$

$\angle Z Y P=116^{\circ}$

Step 2

Since $YQ$ bisects $\angle ZYP$

$\angle Z Y Q=\angle \text { QYP } &=\frac{1}{2} \angle \text { ZYP }$

$&=\frac{1}{2} \times 116^{\circ}$

$&=58^{\circ}$

Also from the figure, it is clear that,

$\angle ZYP = \angle ZYQ + \angle QYP$

And $YQ$ bisect $\angle ZYP,$

Angle $ZYQ$ and $QYP$ are the same.

$\angle ZYP = 2\angle ZYQ$

$\angle ZYP = 116^{0}$

$2 \angle ZYQ = 116^{0}$

$\angle ZYQ = 58^{0}$

$\angle ZYQ$ and $\angle QYP$ is equal to 58°

Step 3

We need to find the value of the angle $XYQ$,

from figure,

$\angle XYQ = \angle XYZ + < \angle ZYQ$

$\angle XYZ = 64^{0}$ and$\angle ZYQ = 58^{0}$

Therefore, the value of angle $XYQ$,

$\angle XYQ = 64 + 58$

$\angle XYQ = 122^{0} .$

Step 4

Need to reflex the angle $QYP$,

$\angle QYP = 180 + \angle XYQ$

$\angle QYP = 180 + 122$

$\angle QYP = 302^{0}$

Hence,$122$° is the value of the angle $XYQ$.

Therefore, the correct answer is $\angle QYP = 302^{0}$ and $\angle XYQ = 122^{0} .$

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