Question

it is given that angle abc = 64 degree and a b is produced to AB
point P draw a figure from the given information if ray BQ bisect angle CBP find angle ABQand reflex angle Q BP

Answer 1

this the diagram
now we BQ bisect the angle CBP
therefore angle QBP = angle CBQ
now angle ABC + angle CBQ + angle QBP = 180
and angle QBP = angle CBQ (given)
solving the equation we get angle CBQ and QBP = 56

Answer 2

A figure with angle abc = 64 degree and a b is produced to AB

point P and ray BQ bisect angle CBP is attached below.

Given,

∠ ABC = 64°

From figure, we have,

∠ ABC + ∠ CBP = 180° (linear pair of angles)

64° + ∠ CBP = 180°

∠ CBP = 180° - 64°

∴ ∠ CBP = 116°

∠ CBQ = ∠ QBP = ∠ CBP / 2

∠ CBQ = ∠ QBP = 116° / 2

∴ ∠ CBQ = ∠ QBP = 58°

Now consider,

∠ ABQ = ∠ ABC + ∠ CBQ

∠ ABQ = 68° + 58°

∴ ∠ ABQ = 126°

Therefore, the reflex angle QBP is given by,

Reflex ∠ QBP = 360° - ∠ QBP

= 360° - 58°

∴ Reflex ∠ QBP = 302°