Question

. ∠POQ=64 , Arm PO is produced up to point R and OS is the bisector of

Answer 1

Answer:

$122$

Step-by-step explanation:

Angle POQ=64. arm PO is produced upto point R and OS is the bisector of Angle QOR. Find the measure of Angle POS.. ∠ POQ = 46 ° Given Let ∠ QOS = x ∠ QOS = ∠ ROS

It is given that line YQ bisects ∠PYZ.

Hence,

∠QYP = ∠ZYQ

PX is straight line

sum of angle in linear pair always equal to 180°

∠XYZ + ∠ZYQ + ∠QYP = 180°

Give that so plug the value we get ∠ XYZ = 64°

And ∠QYP = ∠ZYQ

And ∠QYP = ∠ZYQ

∠ 64° + 2∠QYP = 180°

∠2∠QYP = 180° − 64° = 116°

Divide by 2 we get

∠QYP = 58°

Also, ∠ZYQ = ∠QYP = 58°

Using angle of reflection

∠QYP = 360° − 58° = 302°

∠XYQ = ∠XYZ + ∠ZYQ

= 64° + 58°

= 122°