Question

Could someone help me with this

Answer 1

angle x is 130 degrees

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`