Math, asked by ravisingh53119, 9 months ago

in the given figure angel XYZ=56 and XY is produced to P. if ray YQ bisects Angel ZYP the measure of angel QYP=?​

Answers

Answered by khushiyadav182006
0

Step-by-step explanation:

XYZ=56 degree ( given)

QYZ=QYP (as QY is the bisector of angle ZYP)

XYZ + QYZ+QYP = 180 degree (linear pair)

XYZ +QYP+QYP= 180 degree ( as QYZ =QYP)

XYZ+ 2QYP=180 degree

56 degree + 2QYP= 180 degree

2QYP=180-56 degree

2QYP=124 degree

QYP=124/2

so QYP = 62 degree

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Answered by MissAngry
0

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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