Question

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


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Answer 1

Answer:

Given,

∠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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