Question

р
6. It is given that Z XYZ=64º and XY is produced
to point P. Draw a figure from the given
information. If ray YQ bisects ZZYP, find XYQ
and reflex ZQYP.​

Answer 1

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It is given that Z XYZ=64º and XY is produced

to point P. Draw a figure from the given

information. If ray YQ bisects ZZYP, find XYQ

and reflex ZQYP.

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As angle on a line = 180⁰

➡️∆XYZ + ∆PYZ = 180⁰

➡️∆PYZ = 180 - 64 = 116⁰

As YQ bisects ∆PYZ

➡️∆ZYA = ∆QYP = 58⁰

➡️∆XYQ = 64 + 58 = 122⁰

Reflex ∆QYP - 360⁰ - ∆QYP

= 360 - 58 = { 302⁰ }

Learn more.... Following concepts are only for more information about your Question,

your choice you want to read or not

Concept of Adjacent Angles

Two angles are said to be adjacent when they share a common side and a vertex.

Vertically Opposite Angles

Vertically opposite angles are the angles formed opposite to each other when two lines intersect.

Properties of Transversal

A pair of parallel lines is intersected by a transversal. Following are the properties:

1. Vertically opposite angles are equal. 2. Corresponding angles are equal 3. The interior angles formed on the same side of the transversal are

supplementary.

4. Alternate angles are equal.

Answer 2

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.

Answer :-

i.e : XYP is a straight line.

∴ ∠XYZ + ∠ZYQ + ∠QYP = 180°

⇒ 64° + ∠ZYQ + ∠QYP = 180°

[∵ ∠XYZ = 64° (given)]

⇒ 64° + 2∠QYP = 180°

[YQ bisects ∠ZYP so, ∠QYP = ∠ZYQ]

⇒ 2∠QYP = 180° – 64° = 116°

⇒ ∠QYP = 116°/2 = 58°

∴ Reflex ∠QYP = 360° – 58° = 302°

Since ∠XYQ = ∠XYZ + ∠ZYQ

⇒ ∠XYQ = 64° + ∠QYP [∵∠XYZ = 64°(Given) and ∠ZYQ = ∠QYP]

⇒ ∠XYQ = 64° + 58° = 122° [∠QYP = 58°]

Thus, ∠XYQ = 122° and reflex ∠QYP = 302°.

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