(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^@`.
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