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° and Ray YQ bisects $∠$PYZ.
To Find: $∠$XYQ and Reflex $∠$QYP

It can be observed that PX is a line. Rays YQ and YZ stand on it.
Hence, $∠$XYZ +$∠$ZYP = 180°
By substituting, $∠$XYZ = 64°, we get
64° +$∠$ZYP = 180°
∴ $∠$ZYP = 116°

As YQ bisects $∠$ZYP,
$∠$ZYQ = $∠$QYP
Or $∠$ZYP = 2$∠$ZYQ
∴ $∠$ZYQ = $∠$QYP = 58°

Then $∠$XYQ = $∠$XYZ + $∠$ZYQ
$∠$XYQ = a + 64°
$⇒$ $∠$XYQ = 58° + 64° = 122°.
$∠$XYQ = 122°
Now, reflex $∠$QYP = 180°+$∠$XYQ
Since $∠$XYQ = 122°
we have
∠QYP = 180°+122°
∴ $∠$QYP = 302°