Question

Could someone help me with this

Answer 1

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 $360^o$. There are two angles that are explicitly given: MON = $30^o$, and POR = $80^o$. 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 $30^o$, then MOR = $120^o$.

Now, since the addition of all angles should total $360^o$, we can find what angle "x" measures: $30^o+80^o+120^o+x=360^o\\230^o+x=360^o\\x=360^o-230^o\\x=130^o$