How can we calculate the degree of angle made by the matches? 
I was playing a game on my phone when a question pop up on my screen coming from one of my best mathematics masters:
If we know that all of the matches are in the same size, what would be the alpha's degree?
 A: Consider this diagram.

Looking at isosceles triangles and straight angles, and starting with $\measuredangle{GAH}=\alpha$, we get these facts in this order.
$\measuredangle{AED}=\alpha$
$\measuredangle{ADE}=180°-(\alpha+\alpha)=180°-2\alpha$
$\measuredangle{EDH}=180°-(180°-2\alpha)=2\alpha$
$\measuredangle{DHE}=2\alpha$
$\measuredangle{DEH}=180°-(2\alpha+2\alpha)=180°-4\alpha$
$\measuredangle{GEH}=180°-[\alpha+(180°-4\alpha)]=3\alpha$
$\measuredangle{EGH}=3\alpha$
$\measuredangle{EHG}=180°-(3\alpha+3\alpha)=180°-6\alpha$
$\measuredangle{AHG}=2\alpha+(180°-6\alpha)=180°-4\alpha$
Comparing $\measuredangle{AGH}$ with $\measuredangle{AHG}$,
$180°-4\alpha=3\alpha$
Solving,

$\alpha=\dfrac{180°}7\approx 25.714285714°$

I triple-checked that, with a dynamic diagram in Geogebra (above) and with a trigonometric argument using the law of cosines. I'll skip the details.
A: Let $x$ be the angle in red shown below.
Now using properties of isosceles triangles, express the angle in blue in terms of $x$. Then, express the angle in green (which is also $\alpha$) using the angle in blue. Equate the expression of the angle in green with $180-2x$ (which is also an expression for $\alpha$), and solve for $x$. Finally, substitute $x$ to $180-2x$ to compute $\alpha$.
Sorry for your 'vandalized' diagram. Hope this helps.
