Math, asked by yashawinisingh, 1 month ago

It is given angle XYZ =64° and XY is produce to point P . Draw a figure from the given information . If ray YQ bisect and reflex angle QYP .​

Answers

Answered by gilldeepanshu30
1

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Answered by sachi25
1

Answer:

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°.

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