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Answer:

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Step-by-step explanation:

Solution:

Given: ∠XYZ = 64° and Ray YQ bisects ∠PYZ.

To Find: ∠XYQ and Reflex ∠QYP

When a ray intersects a line, the sum of adjacent angles formed is 180°.

With the given information in the question, we can come up with this diagram.

It is given that ∠XYZ = 64º and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.

Ray YQ bisects ∠ZYP.

Let, ∠ZYQ = ∠QYP = a.

We can see from the figure that PX is a line and YZ is a ray intersecting at point Y and the sum of adjacent angles so formed is 180°.

Hence ∠ZYP + ∠ZYX = 180°

∠ZYQ + ∠QYP + ∠ZYX = 180° [Since, ∠ZYP = ∠ZYQ + ∠QYP]

a + a + 64° = 180°

2a + 64° = 180°

2a = 180° - 64° = 116°

a = 116°/2 = 58°

∴ Then ∠XYQ = ∠XYZ + ∠ZYQ

∠XYQ = a + 64°

⇒ ∠XYQ = 58° + 64° = 122°.

∠XYQ = 122°

As ∠QYP = a,

Thus, Reflex ∠QYP = 360° - a

⇒ 360° - 58° = 302°

Reflex ∠QYP = 302°.

Thus, we have ∠XYQ = 122° and Reflex ∠QYP = 302°.

∠QYP=180

∘

+122

∘

⇒∠QYP=302

∘