Question

it is given that angle xyz is equal to 64 degree and xy is produced to point P .A ray PQ bisectsangle ZYP.draw a figure from the given information.find angle XYQ and reflex angle QYP​

Answer 1

$\huge\tt{Required\:Answer:}$

According to question :

It is given that angle xyz is equal to 64 degree and xy is produced to point P . A ray PQ bisectsangle ZYP. Draw a figure from the given information.

To find :

Find angle XYQ and reflex angle QYP:

Given :

∠XYZ = 64°

=> Hence, ∠XYZ + ∠ZYP = 180° [This is a Linear pair] or

=> 64° + ∠ZYP = 180° or

=> ∠ZYP = 180° - 64° = 116°

here, YQ bisects ∠ZYP :

=> ∠ZYQ = ∠PYQ = ½ ∠ZYP = 116° / 2 = 58°

=> ∠XYQ = ∠XYZ + ∠ZYQ = 64°+ 58° = 122°

=> ∠QYP = 360° - 58° = 302°

Answer 2

Answer:

XYP is a straight line.

→ ∠XYZ + ∠ZYP = 180°

→ ∠ZYP = 180° - 64°

→ ∠ZYP = 116°

∠YQ bisects ∠ZYP

→ ∠ZYQ = ∠PYQ = 1/2 ∠ZYP

→ 1/2 × 116°

→ 58°

→ ∠XYQ = ∠XYZ + ∠ZYQ

→ 64°+ 58°

→ 122°

Now, let us find reflex ∠QYP

→ ∠QYP = 360° - ∠QYP

→ ∠QYP = 360° - 58°

→ 302°