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

∵ Ray YZ stands on line PX
∴ ∠XYZ+ ∠ZYP = 180°
| Linear Pair Axiom

⇒ 64° + ∠ZYP = 180°
| ∵ ∠XYZ = 64° (Given)
⇒ ∠ZYP = 180° - 64°
⇒ ∠ZYP = 116° ...(1)
$because$ Ray YQ bisects $angle ZYP$
$therefore space space angle PYQ equals angle ZYQ equals 1 half angle ZYP equals 1 half left parenthesis 116 degree right parenthesis$
| Using (1)
= 58⁰ ...(2)
$therefore space space angle QYP space equals space 360 degree space minus 58 degree space equals space 302 degree$
$left enclose because$ The sum of all the angles round apoint is equal to 360⁰
Again, $angle XYZ space angle XYZ plus angle ZYQ$
= 64⁰ + 58⁰
$vertical line space because space angle XYZ equals 64 degree$ (Given) and $angle ZYQ equals 58 degree$

[ From (2) ]
= 122⁰.

Some More Questions From Lines and Angles Chapter

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Lines And Angles

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.

Some More Questions From Lines and Angles Chapter

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