1.

6. It is given that angle XYZ=64° and XY is producedto point P. Draw a figure from the giveninformation. If ray YQ bisects angle ZYP, find angle XYQand reflex angle QYP.​

Answer»

ANSWER:

\boxed{ \large\mathtt{answer: \angle{QYP} = 302 \degree}}

#GIVEN,

∠XYZ=64∘

YQ BISECTS ∠ZYP

∠XYZ + ∠ZYP = 180∘ (LINEAR Pair)

64∘ + ∠ZYP = 180∘

∠ZYP = 180° – 64°

∠ZYP = 116∘

#Also, ∠ZYP = ∠ZYQ + ∠QYP

∠ZYQ = ∠QYP (YQbisects∠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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