An octagon is shown.A dotted line extends from each of the points where one side meets another side, so that there are 8 dotted lines meeting at an asterisk in the center of the octagon. These dotted lines divide the octagon into 8 triangles. There is one additional dotted line pointing directly down from the center asterisk. A right angle is formed at the point where this line meets the base of the octagon, in the center of the bottom triangle. The right base angle of this triangle is labeled with a 2. The vertex angle of the triangle directly to the right of this triangle is labeled with a 1. The 2 and the 1 are on either sides of the same dotted line.

Question

What is m<2?
A. 22.5°
B. 45°
C. 60°
D. 67.5°

Answer 1

Since there are 8 equal angles around the center of the octagon, each one measures $\frac{360^\circ}{8}=45^\circ$. Therefore, the vertex angle of the triangle to the right of the triangle with angle 2 is $45^\circ$. Since the three angles in a triangle add up to $180^\circ$, the third angle in this triangle is $180^\circ - 45^\circ - 90^\circ = 45^\circ$. This means that angle 2 and the right base angle of the bottom triangle are equal, so $m<2 = \boxed{\textbf{(B) }45^\circ}$.