Question

Can anyone answer 17-19 for me ??? Please

Answer 1

17.Therefore x=
`31^\circ` and y=
`((123)/(3))^ {\circ}`

18.Therefore x = 9 units and y = 10.5 units

19.Therefore
`x=15^\circ` and y = 7 units

Explanation:

17.

Opposite angles of a parallelogram are equal.

So
`3y^(\circ)=123^(\circ)`

⇒ y=
`((123)/(3))^ {\circ}`

and sum of adjacent angle is =
`180^(\circ)`

Therefore,
`(2x-5)^(\circ) + 123^ {\circ}=180^(\circ)`

⇒
`(2x-5)^(\circ) =180^(\circ)-123^ {\circ}`

⇒
`2x^\circ=57^\circ+5^\circ`

⇒x=
`31^\circ`

Therefore x=
`31^\circ` and y=
`((123)/(3))^ {\circ}`

18.

The diagonals of rectangle bisect each other.

so, 2x=x+9

⇔2x- x=9

⇔x = 9 units

Again opposite sides are congruent.

So,3y -9 =y+12

⇔3y - y =12+9

⇔y
`=(21)/(2)` units =10.5 units

Therefore x = 9 units and y = 10.5 units

19.

`3x^\circ=45^\circ` [∵ they are transversal angles]

⇔
`x=15^\circ`

And opposite sides are equal

7y = 4y + 21

⇔7y - 4y = 21

⇔3y = 21

⇔y = 7 units

Therefore
`x=15^\circ` and y = 7 units