Question

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

Answer 1

Given: ∠XYZ = 64°

Now, ∠XYZ + ∠ZYP = 180°(Linear pair)

Or, 64° + ∠ZYP = 180°

Or, ∠ZYP = 180° - 64° = 116°

Since, YQ bisects ∠ZYP 

So, ∠ZYQ = ∠PYQ = ½ ∠ZYP = 116°/2 = 58°

So, ∠XYQ = ∠XYZ + ∠ZYQ = 64°+ 58° = 122°

Now, reflex ∠QYP = 360° - 58° = 302°

Answer 2

$\underline{ \sf \large{Solution - }}$

Here it is given that,

• ∠XYZ = 64°
• YQ is a bisector of ∠ZYP  

⟶ We have to find the ∠XYQ and reflex ∠QYP

Now,

XYP is a straight line,  

$\sf: \implies \angle XYZ + \angle ZYP = 180 ^ \circ \: \: \: \: \:[Linear \: pair]$

$: \implies \sf \angle ZYP = 180 ^ \circ - \angle XYZ$

$: \implies \sf \angle ZYP = 180 ^ \circ - 64^ \circ$

$: \implies \sf \angle ZYP = 116^ \circ$

Now,  

Since YQ is a bisector of ∠ZYP

$\sf: \implies \angle ZYQ = \angle QYP = \dfrac{1}{2} \: \angle ZYP$

$\sf: \implies \angle ZYQ = \angle QYP = \dfrac{1}{2} \times 116^ \circ$

$\sf: \implies \angle ZYQ = \angle QYP = 58^ \circ$

Now,

$\sf: \implies \angle XYQ = \angle XYZ +\angle ZYQ$

$\sf: \implies \angle XYQ = 64^ \circ +58^ \circ$

$\sf: \implies \boxed{ \sf \angle XYQ =122^ \circ}$

Now,

$\sf: \implies Reflex \: \angle QYP = 360^ \circ - \angle QYP$

$\sf: \implies Reflex \: \angle QYP = 360^ \circ - 58^ \circ$

$: \implies \boxed{\sf Reflex \: \angle QYP = 302^ \circ}$