Question

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

Answer 1

Correct Question :

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

Given :

• ∠XYZ = 64°
• A ray YQ bisects ∠ZYP .

To Find :

• ∠XYQ and reflex QYP .

Solution :

As XYP is a line . So ,

$\longmapsto\tt{x+x+64^{\circ}=180^{\circ}}$

$\longmapsto\tt{2x+64^{\circ}=180^{\circ}}$

$\longmapsto\tt{2x=180^{\circ}-64^{\circ}}$

$\longmapsto\tt{2x=116^{\circ}}$

$\longmapsto\tt{x=\cancel\dfrac{116}{2}}$

$\longmapsto\tt\bf{x=58}$

Value of x is 58 .

Now ,

$\longmapsto\tt{\angle{XYQ}=x+64^{\circ}}$

$\longmapsto\tt{\angle{XYQ}=58+64^{\circ}}$

$\longmapsto\tt\bf{\angle{XYQ}=122^{\circ}}$

Reflex of ∠QYP :

$\longmapsto\tt{360^{\circ}-\angle{QYP}}$

$\longmapsto\tt{360^{\circ}-58^{\circ}}$

$\longmapsto\tt\bf{302^{\circ}}$

Answer 2

Given :-

It is given that XYZ=64° and XY is produced to point P.A ray YQ bisects ZYP°.

To Find :-

XYQ°and reflex OYP°

Solution :-

Sum of linear pair is 180°

∠XYZ + ∠ZYP = 180

64 + ∠ZYP = 180

∠ZYP = 180 - 64

∠ZYP = 116°

YQ is bisecting ∠ZYP

ZYQ and QYP are equal

∠ZYQ = ∠QYP

And ZYQ is half og ZYP

∠ZYQ = ∠ZYP/2

∠ZYQ = 116/2

∠ZYQ = 58°

Finding ∠XYQ

∠XYQ = ∠ZYQ + ∠XYZ

∠XYQ = 58 + 64

∠XYQ = 122°

For

Reflex ∠OYP

Reflex ∠OYP = 360 - ∠OYP

Reflex ∠OYP = 360 - 58

Reflex ∠OYP = 302°