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CBSE Class 9 Mathematics Question 6 of 11

Lines and Angles — Question 6

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Question 6

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.

Answer

The figure is shown below:

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. NCERT Class 9 Mathematics CBSE Solutions.

In the given figure,

Line YQ bisect ∠ZYP.

∴ ∠QYP = ∠ZYQ = x (let) .........(1)

From figure,

⇒ ∠XYZ + ∠ZYQ + ∠QYP = 180° [Linear pairs]

⇒ 64° + x + x = 180° [From equation (1)]

⇒ 64° + 2x = 180°

⇒ 2x = 180° - 64°

⇒ 2x = 116°

⇒ x = 116°2\dfrac{116°}{2}

⇒ x = 58°.

⇒ ∠ZYQ = ∠QYP = x = 58°

Reflex ∠QYP = 360° - ∠QYP = 360° - 58° = 302°.

From figure,

⇒ ∠XYQ = ∠XYZ + ∠ZYQ

= 64° + 58°

= 122°.

Hence, ∠XYQ = 122° and Reflex ∠QYP = 302°.