(a) Find `x+y+z` (b) Find `x+y+z+w`

Explanation

(a) Sum of linear pair of angles is=`180^@`
`x+90^@=180^@`
`x=180^@-90^@`
`x=90^@`
And`z+30^@=180^@`(linearpair
And
`y=90^@+30^@`(exteriorangletheorem)
`y=120^@`
`x+y+z=90^@+120^@+150^@`
`=360^@`
(b) Find x +y +z +wThe sum of the measures of
all the interior angles of a quadrilateral is 360º.
Using the angle sum property of a quadrilateral,
Let n is the fourth interior angle of the quadrilateral.
`60^@+80^@ +120^@ + n = 360^@`
`260^@ + n = 360^@`
`n = 360^@- 260^@`
`n = 100^@`
sum of linear pair of angles is `180^@` .
`w+100^@=180^@` ...(1)
`x+120^@=180^@` .....(2)
`y+80^@=180^@` ....(3)
`z+60^@=180^@` ...(4)
Adding equation (1), (2), (3) and (4),
`w+100^@+x+120^@+y+80^@+z+60^@=180^@+180^@+180^@+180^@`
`w+x+y+z+360^@=720^@`
`w+x+y+z=720^@-360^@`
`w+x+y+z=360^@`
The sum of the measures of the external angles of any polygon is `360^@`.