Since the octagon is regular, all of its angles are equal. Let this angle be $x$. Since angle 2 is a right angle, triangle 2 must be a 45-45-90 triangle, meaning angle 2 is 45 degrees. Therefore, angle 1 is $180^\circ - 90^\circ - x = 90^\circ - x$.
We can use the fact that the dotted lines divide the octagon into triangles and use the formula for the sum of angles in a polygon to get $8\cdot (180^\circ - 2x) + 360^\circ = 6(180^\circ)$, since there are 8 triangles formed and one additional 360 degree angle at the center. Simplifying, we get $x = 135^\circ$.
Therefore, angle 1 is $90^\circ - 135^\circ = \boxed{\textbf{(A) } 22.5^\circ}$.
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.
The figure above is a regular octagon with radii and an apothem drawn. What is mangle1?
A. 22.5°
B. 45°
C. 60°
D. 67.5°
3 answers
thank you bot!
You're welcome! Don't hesitate to ask if you have any more questions.
1 answer