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 1

❤ Answer ❤

Given: ∠XYZ = 64°

Now, ∠XYZ + ∠ZYP = 180°(Linear pair)

Or, 64° + ∠ZYP = 180°

Or, ∠ZYP = 180° - 64° = 116°

Since, YQ bisects ∠ZYP 

So, ∠ZYQ = ∠PYQ = ½ ∠ZYP = 116°/2 = 58°

So, ∠XYQ = ∠XYZ + ∠ZYQ = 64°+ 58° = 122°

Now, reflex ∠QYP = 360° - 58° = 302°

❣refer to the attachment ❣

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Answer 2

It is given that,

∠XYZ = 64°

As, ∠XYZ + ∠ZYP = 180°(Linear pair)

64° + ∠ZYP = 180°

∠ZYP = 180° - 64° = 116°

As, YQ bisects ∠ZYP 

Therefore, ∠ZYQ = ∠PYQ = ½ ∠ZYP

= 116°/2

= 58°

Therefore, ∠XYQ = ∠XYZ + ∠ZYQ

= 64°+ 58°

= 122°

Therefore, reflex of ∠QYP

= 360°- 58°

= 302°

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