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
XYP is a straight line,
∠XYZ+∠ZYP=180∘(linear pair)
∠ZYP=180∘−∠XYZ=180∘−64∘=116∘
Since YQ bisects ∠ZYP
∠ZYQ=∠QYP=12∠ZYP=12×116∘=58∘
∠XYQ=∠XYZ+∠ZYQ=64∘+58∘=122∘
We have to find reflex∠QYP
Reflex∠QYP=360∘−∠QYP=360∘−58∘=302∘