As shown in a figure, there are the right hexagon ABCDEF and a right heptagon ABGHIJK.
Find the angle of X and Y.
Find the angle of X and Y.
Answer
X = 900/7 - 120 = 60/7 degrees.
Figure is an enlarged figure of the upper part of the figure in question.
The point O is the intersection of the side ED and the line which is drawn by being extended the line being connected L and vertex I of right heptagon.
Since ∠MEO=∠NDO = 60 degrees, △ LED is an equilateral triangle.
Thus, as for △LMI, ∠MLI = 60 / 2 = 30 degree and ∠MIL = (360 - One of interior angle of the right heptagon) / 2 = (360 - 900/7) / 2 = 810/7 degrees.
Therefore, Y = ∠LMI = 180 - 30 - 810/7 = 240/7 degrees.
X = 60/7 degrees
Y = 240/7 degrees
Y = 240/7 degrees
Solution
One of Interior angle of the right hexagon is 120 degrees and that of right heptagon is
180 - (360/7) = 900/7 degrees.
180 - (360/7) = 900/7 degrees.
X = 900/7 - 120 = 60/7 degrees.
Figure is an enlarged figure of the upper part of the figure in question.
The point L is an intersection of extended upwards the side EF and DC of the right hexagon.
The point O is the intersection of the side ED and the line which is drawn by being extended the line being connected L and vertex I of right heptagon.
Since ∠MEO=∠NDO = 60 degrees, △ LED is an equilateral triangle.
Thus, as for △LMI, ∠MLI = 60 / 2 = 30 degree and ∠MIL = (360 - One of interior angle of the right heptagon) / 2 = (360 - 900/7) / 2 = 810/7 degrees.
Therefore, Y = ∠LMI = 180 - 30 - 810/7 = 240/7 degrees.
