Answer:
angle x is 130 degrees
Step-by-step explanation:
Recall that the addition of all central angles of the full circle should add up to [tex]360^o[/tex]. There are two angles that are explicitly given: MON = [tex]30^o[/tex], and POR = [tex]80^o[/tex]. The other piece of information is that the arc from M to R is 4 times the length of the smaller arc From N to M, and therefore, their angles should keep the same proportion. That is: angle MOR should be 4 times angle MON, which in math terms will be: MOR = 4 x [tex]30^o[/tex], then MOR = [tex]120^o[/tex].
Now, since the addition of all angles should total [tex]360^o[/tex], we can find what angle "x" measures: [tex]30^o+80^o+120^o+x=360^o\\230^o+x=360^o\\x=360^o-230^o\\x=130^o[/tex]
