Question

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It is given that angle XYZ=64⁰ and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects angle ZYP,find angle angle XYQ and reflex angle 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°

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Answer 2

Answer:

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