Answer:
i) C; x=y= 80°, ii) B; x= 58°, iii) D; x= 62° and y= 56°, iv) D; none of these are correct.
Step-by-step explanation:
i) Full angle around is 360°
As given one angle is 100°,which means vertically opposite angles are equal to 100°
Now, remaining angle is equal to [tex]360-200= 160°[/tex]
∵ x and y are vertically opposite angle, which means they are equal.
∴x=y= 80°
ii) As we know straight angle is equal 180°
As given one of the angle is 32° and other says, it is a right angle which is equal to 90°.
∴ ∠x= [tex]180-(90+32)= 58°[/tex]
∴∠x= 58°
iii) Full angle = 360°
2∠x = 124° (∵ Vertically opposite angle are equal )
⇒∠x= [tex]\frac{124}{2}[/tex]
∴∠x= 62°
∠x+∠x+∠y= 180° (∵ it is a straight angle)
2∠x+∠y= 180°
⇒[tex]124+ y= 180[/tex]
Subtracting both side by 124
⇒∠y= [tex]180-124= 56°[/tex]
∴∠y= 56°
iv) Full angle= 360°
∴ ∠x+22°+32°+51°= 360°
Subtracting both side by 105
∠x= [tex]360-105= 255°[/tex]
∴∠x= 255°
Which means none of the given option are correct.
