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

Given,

∠XYZ=64°

YQ bisects ∠ZYP

∠XYZ+∠ZYP=180° (Linear Pair)

⇒64

+∠ZYP=180°

∠ZYP=116°

Also, ∠ZYP=∠ZYQ+∠QYP

∠ZYQ=∠QYP (YQ bisects∠ZYP)

⇒∠ZYP=2∠ZYQ

⇒2∠ZYQ=116°

⇒∠ZYQ=58°

=∠QYP

Now, ∠XYQ=∠XYZ+∠ZYQ

⇒∠XYQ=64°+58°

⇒∠XYQ=122°

Also, reflex ∠QYP=180° +∠XYQ

∠QYP=180 +122

⇒∠QYP=302∘

Answer 2

Answer:

Given,

∠XYZ=64∘

YQ bisects ∠ZYP

∠XYZ+∠ZYP=180∘(Linear Pair)

⇒64∘+∠ZYP=180∘

∠ZYP=116∘

Also, ∠ZYP=∠ZYQ+∠QYP 

∠ZYQ=∠QYP   (YQ bisects∠ZYP)

⇒∠ZYP=2∠ZYQ

⇒2∠ZYQ=116∘

⇒∠ZYQ=58∘=∠QYP

Now, ∠XYQ=∠XYZ+∠ZYQ

⇒∠XYQ=64∘+58∘

⇒∠XYQ=122∘

Also, reflex ∠QYP=180∘+∠XYQ

∠QYP=180∘+122∘

⇒∠QYP=302∘

thank you

by

_vaishnavi