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# hard geometry

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You have a triangle with 45 identical lines in this way as you can see on the picture.

What is gamma?

Jul 17, 2020

#1
+25568
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You have a triangle with 45 identical lines in this way as you can see on the picture.

What is gamma?

$$\begin{array}{|r|r|} \hline & angle \\ \text{lines} & =\dfrac{\text{lines}-1}{2} \\ \hline 5 & 2\gamma \\ 7 & 3\gamma \\ 9 & 4\gamma \\ 11 & 5\gamma \\ 13 & 6\gamma \\ 15 & 7\gamma \\ \ldots & \ldots \\ 45 & \dfrac{\text{45}-1}{2}=22\gamma\\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline 2*22\gamma+\gamma &=& 180^\circ \\ 45\gamma &=& 180^\circ \\ \gamma &=& \dfrac{180^\circ}{45} \\ \mathbf{\gamma} &=& \mathbf{ 4} \\ \hline \end{array}$$

Jul 17, 2020