Question

Help me please? Circles & angles. http://i.imgur.com/K65u1KO.png

Answer 1

This is what is called for as "interior angle".
you see, an interior angle defines two angles, the second being the prolongation of the segments that composes the original angle.
Let's take for instance a circumference "C" ang an arbitrary interior angle \( \beta \).
The angle \( \beta \) will define then four points on "C" due to the prolongation of the segments composing \( \beta \).

So, what will be a consequence of this will be that \( \beta \) will then define two arches, and these two arches being: \(arc. AB\) and \(arc.xy\).
Then, we can calculate angle \( \beta \) by the following formula:
\[\beta = \frac{ arc.xy+arcAB }{ 2 }\]
This formula is only applicable when \( \beta \) is an internal angle that is not the central angle, well, it is applicable but you'll end up getting the same value for any \( \alpha\) that is a central angle.

Answer 2

So, on your math excercise, you have to apply the formula I stated above:
\[x= \frac{ arc.BC+arc.AD }{ 2 }\]
And replace the arches for their corresponding values:
\[x=\frac{ 90+140 }{ 2 }\]
Operating this will give you the value for "x" thus solving the problem.
I'll leave that part to you.

Answer 3

Oooo. So ...

x = 230/2

x = 115 ?

Answer 4

Yes that's correct.

Answer 5

@Owlcoffee Thank you so much. :) You're amazing!!