Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

25. 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.

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

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

⇒ 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 $angle ZYQ equals 58 degree$