Question

It is given angle XYZ =64° and XY is produce to point P . Draw a figure from the given information . If ray YQ bisect and reflex angle QYP .​

Answer 1

Answer:

XYZ=64 ∘

YQ bisects ∠ZYP

∠XYZ+∠ZYP=180 ∘

(Linear Pair)

⇒64 ∘

+∠ZYP=180 ∘

∠ZYP=116 ∘

Also, ∠ZYP=∠ZYQ+∠QYP

∠ZYQ=∠QYP (YQ bisects∠ZYP)

⇒∠ZYP=2∠ZYQ

⇒2∠ZYQ=116 ∘

⇒∠ZYQ=58 ∘

=∠QYP

Now, ∠XYQ=∠XYZ+∠ZYQ

⇒∠XYQ=64 ∘

+58 ∘

⇒∠XYQ=122 ∘

Also, reflex ∠QYP=180 ∘

+∠XYQ

∠QYP=180 ∘

+122 ∘

⇒∠QYP=302 ∘

Step-by-step explanation:

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Answer 2

Answer

$\angle \: ZYP + \angle XYZ = 180°$

$⇒ \angle XYP + 64°=180°$

$⇒\angle ZYP = 116°$

$⇒\angle XYQ = \frac{1}{2} \angle ZYP$

$⇒ \frac{1}{2} \times 116° = 58°$

$\colorbox{ligeen} {Reflex }\angle XYQ = 360° - 58° = 302°$

Additional Information:-

Before solving this question, let us know about angle bisectors.ANGLE BISECTOR: A line that splits an angle into two equal angles is called an angle bisector.('bisect' means to divide into two equal parts)So, the angle bisector of 64° will divide it into two equal halves, measuring 32° each.Complete step-by-step answer:Let us solve this question now.Draw an angle of 64° and name it XYZ.Now, extend the line segment XY till P.Now, make a ray YQ, which bisects angle ZYP.Now, let us find the angle XYQ.We can see that YQ is bisecting the angle ZYP, whose measure is 64°. So, the measure of XYQ and ZYQ would be 32° each So, the measure of XYQ is 32°.Let us now find the value of QYP.We can see that XP is an extension of YX. And, the measure of an angle does not change if the arm of the angle is extended. So, the measure of the angle QYP will be the same as that of the angle XYP.So, the measure of the angle QYP is 32°.

Note:- One must make all the angles properly in this question. As, if there is a mistake in the measure of any angle, then the whole answer will come out to be wrong. Make sure that YQ ray bisects the acute angle XYZ.

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