Question

Find the measure of wzx. Show your work.​

Answer 1

Attached

Explanation:

Answer 2

Part 17)
`1,800^o`

Part 18)
`\angle WZX=77^o`

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

`S=(n-2)180^o`

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

`S=(12-2)180^o`

`S=(10)180^o`

`S=1,800^o`

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

`(18x+5)^o=48^o+(8x-3)^o`

solve for x

Group terms

`18x-8x=48-3-5`

Combine like terms

`10x=40`

`x=4`

step 2

Find the measure of angle WZX

`\angle WZX=(18x+5)^o`

substitute the value of x

`\angle WZX=(18(4)+5)=77^o`