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It is given that ∠XYZ=64∘ and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.

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302

°

and 122

°

122

°

and 302

°

120

°

and 300

°

300

°

and 120

°

answer is A.

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Detailed Solution

⇒∠XYZ + ∠ZYP = 180

°

⇒∠ZYP =180

°

−∠XYZ
⇒∠ZYP = 180

°

−64

°

⇒∠ZYP = 116

°

Now since YQ bisects ∠ZYP
Therefore, the equation will become
⇒∠ZYQ=∠QYP =

\frac{1}{2}

∠ZYP
⇒∠ZYQ=∠QYP =

\frac{1}{2}

×116

°

⇒∠ZYQ=∠QYP=58

°

Since, ∠XYQ = ∠XYZ+∠ZYQ
⇒∠XYQ=64

°

+58

°

∠XYQ = 122

°

Now we have to find the reflex angle ∠QYP
Reflex ∠QYP = 360

°

−∠QYP
Reflex ∠QYP = 360

°

−58

°

Reflex ∠QYP = 302

°

Therefore, Reflex ∠QYP=302

°

and ∠XYQ=122

°

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