Question

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

Answer 1

Given : -

It is given that angle XYZ = 64° and XY is produced to point P. Draw the figure from given information. If Ray YQ bisects angle ZYP.

To Find : -

XYQ and reflex angle QYP .

Step-by-step Explanation : -

XYP is a Line.

( Refer to the Attachment )

On Calculating : -

y + y + 64 = 180°

2y + 64 = 180

2y = 180 - 64

2y = 116

y = 116/2

y = 58

Now : -

∠XYQ = y + 64

58 + 64

122°

Reflex ∠QYP = 360° - ∠QYP

360° - 58

302°

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 :-

ie : 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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