Question

It is given that 2 XYZ= 64° and XY is produced
to point P. Draw a figure from the given
information. If ray YQ bisects ZZYP, find Z XYQ
and reflex ZQYP​

Answer 1

Step-by-step explanation:

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∘