Find the values of the unknowns x and y in the following diagrams

Explanation

`x = 120^@`
`x = 120^@ − 50^@`
`x = 70^@`

By angle sum property,Sum ofinteriorangles`=180^@`
`50^@+70^@+x=180^@`(i)We know that, Sum of interior opposite angles of a triangle = Exterior angle

`50^@ + 120^@ + x= 180^@`
`x = 180^@ − 120^@`
`x = 60^@`

(ii)`x=80^@`(verticallyopposite angles)By angle sum property
Sum of interior angle=`180^@`(verticallyopposite angles)By angle sum property
Sum of interior angles
` = 180^@`
`50^@ + x + 80^@ = 180^@`
`50^@ + x + 80^@= 180^@`
`130^@ + x = 180^@`
`x = 180^@ − 130^@`
`x = 50^@ `
(iii)Solve for x and y
We know that, Sum of interior opposite angles of a triangle = Exterior angle
`50^@ + 60^@ = x`
`110^@ = x`
`x = 110^@`
By angle sum property,Sum of interior angles = 180^@
`50^@ + 60^@+y=180^@`
`110^@ + y=180^@`
`y = 180^@ −110^@`
`y= 70^@`
(iv)Solve for x and y`x = 60^@ `(vertically opposite angles are equal)
We know that,

Sum of interior angles of a triangle` =180^@`

`30^@ + x + y = 180^@`

`30^@ + 60^@ + y = 180^@`
`90^@ + y = 180^@`
`y = 180^@ − 90^@`
`y = 90^@`

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