In the figure ● is a point divides the circumference into nine equally.
Find the angle of X.
Answer
100 degrees
Solution
Auxiliary lines are drawn as shown in a figure below.
The most inside figure turns into a right nonagon according to symmetry of the figure.
Moreover, triangle ABC becomes an isosceles triangle.
One of the exterior angle of the right nonagon is 360/9 = 40 degrees.
Therefore, X = 180 - 40 × 2 = 100 degrees.
Find the angle of X.
Answer
100 degrees
Solution
Auxiliary lines are drawn as shown in a figure below.
The most inside figure turns into a right nonagon according to symmetry of the figure.
Moreover, triangle ABC becomes an isosceles triangle.
One of the exterior angle of the right nonagon is 360/9 = 40 degrees.
Therefore, X = 180 - 40 × 2 = 100 degrees.
