Question

${\mathfrak{\red{\clubs{\large{\underline{Question}}}}}}$
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 of angle QYP.


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Answer 1

Step-by-step explanation:

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

this is your answer.

Given,

Given,∠XYZ=64°

Given,∠XYZ=64°YQ bisects ∠ZYP

Given,∠XYZ=64°YQ bisects ∠ZYP∠XYZ+∠ZYP=180°

Given,∠XYZ=64°YQ bisects ∠ZYP∠XYZ+∠ZYP=180°(Linear Pair)

Given,∠XYZ=64°YQ bisects ∠ZYP∠XYZ+∠ZYP=180°(Linear Pair)⇒64°+∠ZYP=180°

Given,∠XYZ=64°YQ bisects ∠ZYP∠XYZ+∠ZYP=180°(Linear Pair)⇒64°+∠ZYP=180°∠ZYP=116°

Given,∠XYZ=64°YQ bisects ∠ZYP∠XYZ+∠ZYP=180°(Linear Pair)⇒64°+∠ZYP=180°∠ZYP=116°Also, ∠ZYP=∠ZYQ+∠QYP

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)

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

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°

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°

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

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°=∠QYPNow, ∠XYQ=∠XYZ+∠ZYQ

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°=∠QYPNow, ∠XYQ=∠XYZ+∠ZYQ⇒∠XYQ=64°+58°

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°=∠QYPNow, ∠XYQ=∠XYZ+∠ZYQ⇒∠XYQ=64°+58°⇒∠XYQ=122°

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°=∠QYPNow, ∠XYQ=∠XYZ+∠ZYQ⇒∠XYQ=64°+58°⇒∠XYQ=122°Also, reflex ∠QYP=180° +∠XYQ

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°=∠QYPNow, ∠XYQ=∠XYZ+∠ZYQ⇒∠XYQ=64°+58°⇒∠XYQ=122°Also, reflex ∠QYP=180° +∠XYQ∠QYP=180°+122°

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°=∠QYPNow, ∠XYQ=∠XYZ+∠ZYQ⇒∠XYQ=64°+58°⇒∠XYQ=122°Also, reflex ∠QYP=180° +∠XYQ∠QYP=180°+122°⇒∠QYP=302°.

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