Answer:
Part 1) The measure of angle Z is [tex]87\°[/tex]
Part 2) The measure of angle x is [tex]82\°[/tex]
Part 3) The measure of angle y is [tex]98\°[/tex]
Step-by-step explanation:
we know that
In a inscribed quadrilateral opposite angles are supplementary
so
In this problem
[tex]93\°+z=180\°[/tex] ------> equation A
[tex]x+y=180\°[/tex]----> equation B
step 1
Find the measure of angle Z
Solve the equation A
[tex]93\°+z=180\°[/tex]
solve for z
[tex]z=180\°-93\°=87\°[/tex]
step 2
Find the measure of angle x
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<x=\frac{1}{2}(58\°+106\°)= 82\°[/tex]
step 3
Find the measure of angle y
Solve the equation B
[tex]x+y=180\°[/tex]
we have
[tex]x=82\°[/tex]
substitute
[tex]82\°+y=180\°[/tex]
[tex]y=180\°-82\°=98\°[/tex]
