Polygon angle

A regular 15-angle is given. A triangle is formed if we connect points 3 and 7, 13 and 10. The vertices are 3 and 13, and the lines' intersections are 3.7 and 13.10. We are to determine the angle size formed by sides 3.7 and 13.10. These numbers indicate the vertices of the 15-gon.

Final Answer:

a =  24 °

Step-by-step explanation:

$$\begin{gathered} u=360/15=24 \\ {u}_1=(7-3)\cdot u=(7-3)\cdot 24=96 \\ {u}_2=(10-7)\cdot u=(10-7)\cdot 24=72 \\ {u}_3=(13-10)\cdot u=(13-10)\cdot 24=72 \\ b=180-(90-u_1/2)-(90-u_2/2)=180-(90-96/2)-(90-72/2)=84 \\ c=180-(90-u_2/2)-(90-u_3/2)=180-(90-72/2)-(90-72/2)=72 \\ a=180-(b+c)=180-(84+72)=24^{\circ } \end{gathered}$$

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