Question

It is given that angle XYZ= 64° and XY is produced
to point P. Draw a figure from the given
information. If ray YQ bisects angleZYP, find angleXYQ
and reflex angleQYP​

Answer 1

Answer:

Step-by-step explanation:

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°

Answer 2

x+x+ 64=180

2x+64=180

2x=180-64=116

x=58

angleXYQ=x +64=58+64=122 degree

angle YQP= x degree= 58degree

reflex =angleYQP=360-58=300degree