Question

Find the value of x in the figure below. Show all steps.

Answer 1

Oh, Geometry can be a little a tricky, but Let's make it a little proof, shall we?

Now I will have to make a construction, I'll join the AC segment, they will form me other two angles wich I'll call "z" and "y":

Now, there is a theorem that will be useful here, that states that the sum of x and z would give me the exact value of "y",
so, basing it on our drawing we say:
\[y=x+y\]
So let's solve it for "x":
\[x=y-z\]
And the properties that hold the angles, "y" and "z" are:
\[<y=\frac{ ArcDA }{ 2 }\]
\[<z=\frac{ ArcCB }{ 2 }\]
Then:
\[x=(\frac{ ArcDA }{ 2 })-(\frac{ ArcCB }{ 2 })\]
\[x=\frac{ ArcDA-ArcCB }{ 2 }\]
And there we have it, very small proof, but the one that can help to solve the problem.