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.
Lines & Angles
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Question

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.

KnowledgeBoat · Accepted Answer

The figure is shown below: 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 = ⇒ 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°.

Mathematics

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.

Lines & Angles

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