Question

It is given that _ XYZ=64° and XY is produced to point P. A ray YQ bisects Z ZYP.
Draw a figure from the given information. Find Z XYQ and reflex ZQYP.​

Answer 1

Answer:

∠XYZ=64

∘

YQ bisects ∠ZYP

∠XYZ+∠ZYP=180

∘

(Linear Pair)

⇒64

∘

+∠ZYP=180

∘

∠ZYP=116

∘

Also, ∠ZYP=∠ZYQ+∠QYP

∠ZYQ=∠QYP (YQ bisects∠ZYP)

⇒∠ZYP=2∠ZYQ

⇒2∠ZYQ=116

∘

⇒∠ZYQ=58

∘

=∠QYP

Now, ∠XYQ=∠XYZ+∠ZYQ

⇒∠XYQ=64

∘

+58

∘

⇒∠XYQ=122

∘

Also, reflex ∠QYP=180

∘

+∠XYQ

∠QYP=180

∘

+122

∘

⇒∠QYP=302

∘

solution

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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