Question

Please solve much appreciated

Answer 1

i) C; x=y= 80°, ii) B; x= 58°, iii) D; x= 62° and y= 56°, iv) D; none of these are correct.

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
`360-200= 160°`

∵ 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=
`180-(90+32)= 58°`

∴∠x= 58°

iii) Full angle = 360°

2∠x = 124° (∵ Vertically opposite angle are equal )

⇒∠x=
`(124)/(2)`

∴∠x= 62°

∠x+∠x+∠y= 180° (∵ it is a straight angle)

2∠x+∠y= 180°

⇒
`124+ y= 180`

Subtracting both side by 124

⇒∠y=
`180-124= 56°`

∴∠y= 56°

iv) Full angle= 360°

∴ ∠x+22°+32°+51°= 360°

Subtracting both side by 105

∠x=
`360-105= 255°`

∴∠x= 255°

Which means none of the given option are correct.