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jahnvi87
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Asked: 2023-03-23T04:00:10+00:00 In:

It is given that ∠ XYZ = 64° and XY is produced to point P.

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Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠ QYP.

NCERT Class 9 mathematics chapter 6
Page No. 97
Exercise 6.1
Question No. 6

chapter 6class 9ncert
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    1. Best Answer
      It is given that ∠ XYZ = 64° and XY is produced to point P.

      ∠PYZ + ∠XYZ = 180° [∵ Linear Pair]
      ⇒ ∠PYZ + 64° = 180° [∵ ∠XYZ = 64°]
      ⇒ ∠PYZ = 180° – 64° = 116°
      But,
      ∠PYQ = ∠ZYQ = 1/2 ∠PYZ [∵ ∠ZYP is bisected by ray YQ]
      ∴ ∠PYQ = ∠ZYQ = 1/2 × 116° = 58°
      ∴ ∠XYQ = ∠XYZ + ∠ZYQ = 64° + 58° = 122 and
      Reflex ∠QYP = 360° – ∠QYP = 360° – 58° = 302°

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