Question 954475
For a decagon (n=no. of sides=10)
{{{((n-2)(180))/n}}}=interior angle
{{{((8)(180))/10}}}=144 degrees 
Interior and exterior angles are supplementary so exterior angles are 36 degrees. 
Angle XBD and Angle XCB are each 36 degrees, so Angle BXC is the third angle of the triangle =180-72=108 degrees 
From the midpoint of side BC to X is one leg of a right triangle, from midpoint to B is the other leg and BX is hypotenuse. Length of B to midpoint is (1/2)20cm=10cm so cos(36)=10cm/BX, BX=10cm/cos(36)=12.36cm 
ANSWER: BX=12.36 cm