6. 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. Solution:
Here, XP is a straight line So, ∠XYZ +∠ZYP = 180° Putting the value of ∠XYZ = 64° we get, 64° +∠ZYP = 180° ∴ ∠ZYP = 116° From the diagram, we also know that ∠ZYP = ∠ZYQ + ∠QYP Now, as YQ bisects ∠ZYP, ∠ZYQ = ∠QYP Or, ∠ZYP = 2∠ZYQ ∴ ∠ZYQ = ∠QYP = 58° Again, ∠XYQ = ∠XYZ + ∠ZYQ By putting the value of ∠XYZ = 64° and ∠ZYQ = 58° we get. ∠XYQ = 64°+58° Or, ∠XYQ = 122° Now, reflex ∠QYP = 180°+XYQ We computed that the value of ∠XYQ = 122°. So, ∠QYP = 180°+122° ∴ ∠QYP = 302°
