MATHEMATICS ENCYCLOPEDIA

AB and CD intersect each other at O. Given ∠EOA = 90°, ∠EOC = x, ∠BOC = y and ∠BOD = 2y + 30. Find the value of x and y and ∠AOD Since CD is a straight line, therefore the sum of 2y + 30 and y must be 180 degree Hence, 2y + 30 + y = 180 3y + 30 = 180 3y = 150   y = 50° Also AB is a straight line therefore the sum of angles EOA, EOC and BOC must be 180 degree. Hence, 90 + x + y = 180 90 + x + 50 = 180  x + 140 = 180 x = 40° Therefore, x = 40° and y = 50°.

Find a, b and c from the following figure below Since CD is a straight line, therefore the sum of angles 4x, 3x and 5x must be 180° Hence, 4x + 3x + 5x = 180 →  12x = 180 →  x = 15 ° Now, we see that following are the equal angles because they are vertically opposite, hence  a = 5x  b = 3x  c = 4x Therefore,    a = 5x = 5*15 = 75°   b = 3x = 3*15 = 45 °  c = 4x = 4*15 = 60 °

The magic hexagon, the following is the only known magic hexagon ever. There are no other magic hexagon of any size. Size of the magic hexagon Properties of the magic hexagon