Answer:
Part 1) [tex]z=121^o[/tex]
Part 2) [tex]x=59^o[/tex]
Part 3) [tex]y=49^o[/tex]
Part 4) [tex]w=72^o[/tex]
Step-by-step explanation:
step 1
Find the measure of angle z
we know that
The sum of exterior angles in a polygon is always equal to 360 degrees
so
[tex]z^o+(z+10)^o+(z-13)^o=360^o[/tex]
solve for z
[tex](3z-3)^o=360^o[/tex]
[tex]3z=363\\z=121^o[/tex]
step 2
Find the measure of angle x
we know that
[tex]z^o+x^o=180^o[/tex] ---> by supplementary angles (form a linear pair)
we have
[tex]z=121^o[/tex]
substitute
[tex]121^o+x^o=180^o[/tex]
[tex]x=180^o-121^o=59^o[/tex]
step 3
Find the measure of angle y
we know that
[tex]y^o+(z+10)^o=180^o[/tex] ---> by supplementary angles (form a linear pair)
we have
[tex]z=121^o[/tex]
substitute
[tex]y^o+(121+10)^o=180^o[/tex]
[tex]y=180^o-131^o=49^o[/tex]
step 4
Find the measure of angle w
we know that
[tex]w^o+(z-13)^o=180^o[/tex] ---> by supplementary angles (form a linear pair)
we have
[tex]z=121^o[/tex]
substitute
[tex]w^o+(121-13)^o=180^o[/tex]
[tex]w=180^o-108^o=72^o[/tex]
