The measure of an interior angle of a regular $n$-sided polygon is calculated as $\frac{(n-2) \cdot 180^{\circ}}{n}$. Öykü draws a regular $k$-sided polygon with a red pen in her notebook. On each side of this polygon, she draws an equilateral triangle as shown in Figure 1, with one side length equal to the side length of the polygon. Then Öykü connects the vertices of these triangles that are not on the red colored sides with a blue pen in a straight line. When she does this, she obtains another regular polygon, and she measures one of the resulting angles as $42^{\circ}$ as shown in Figure 2. According to this, what is $k$? A) 8 B) 9 C) 10 D) 11 E) 12
The measure of an interior angle of a regular $n$-sided polygon is calculated as $\frac{(n-2) \cdot 180^{\circ}}{n}$.
Öykü draws a regular $k$-sided polygon with a red pen in her notebook. On each side of this polygon, she draws an equilateral triangle as shown in Figure 1, with one side length equal to the side length of the polygon.
Then Öykü connects the vertices of these triangles that are not on the red colored sides with a blue pen in a straight line. When she does this, she obtains another regular polygon, and she measures one of the resulting angles as $42^{\circ}$ as shown in Figure 2.
According to this, what is $k$?
A) 8
B) 9
C) 10
D) 11
E) 12