Answer:
Part 17) [tex]1,800^o[/tex]
Part 18) [tex]\angle WZX=77^o[/tex]
Step-by-step explanation:
Part 17) What is the sum of the measures of the interior angles of a dodecagon?
we know that
The sum of the interior angles in a polygon is equal to
[tex]S=(n-2)180^o[/tex]
where
n is the number of sides of polygon
In this problem we have
n=12 sides (dodecagon)
substitute the value of n in the formula
[tex]S=(12-2)180^o[/tex]
[tex]S=(10)180^o[/tex]
[tex]S=1,800^o[/tex]
Part 18) Find the measure of angle WZX
step 1
Find the value of x
we know that
An exterior angle of a triangle is equal to the sum of the opposite interior angles
so
[tex](18x+5)^o=48^o+(8x-3)^o[/tex]
solve for x
Group terms
[tex]18x-8x=48-3-5[/tex]
Combine like terms
[tex]10x=40[/tex]
[tex]x=4[/tex]
step 2
Find the measure of angle WZX
[tex]\angle WZX=(18x+5)^o[/tex]
substitute the value of x
[tex]\angle WZX=(18(4)+5)=77^o[/tex]
