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In the figure given below, it is given that $∠ X Y Z = 64 °$ and XY is produced to point P.
If ray YQ bisects $∠ Z Y P$ , then what are the values of $∠ X Y Q$ and reflex $∠ Q Y P$ respectively?

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An Intiative by Sri Chaitanya

132 ° and 302 °

122 ° and 2 02 °

152 ° and 302 °

122 ° and 302 °

answer is D.

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Detailed Solution

Given data,

∠ X Y Z = 64 °

and XY is produced to point P such that the ray YQ bisects

∠ Z Y P .

Since XYP is a straight line, so the sum of all angles made on it is 180°.
Question Image

⇒ 2 ∠ Q Y P = 180 ° − 64 ° ⇒ ∠ Q Y P = 116 ° 2 = 58 °

Therefore, from equation (1),

Now, the reflex

∠ Q Y P = 360 ° − 58 ° = 302 ° .

From the figure, we have,

∠ X Y Q = ∠ X Y Z + ∠ Z Y Q

Substituting the value of

∠ X Y Z = 64 ° and ∠ Z Y Q = 58 °

, we get,

∠ X Y Q = 64 ° + 58 ° ⇒ ∠ X Y Q = 122 °

Therefore, the values of

∠ X Y Q = 122 °

and reflex

∠ Q Y P = 302 ° .

Hence, option (4) is correct.

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