Mathematics Question and Solution
Calculating Angle x.
Let the base of the ascribed quadrilateral be 1 unit.
(1/sin78) = (a/sin(18+30))
a = 0.75974712295 units.
(1/sin78) = (b/sin54)
b = 0.82709091529 units.
(0.82709091529/sin30) = (c/sin18)
c = 0.51117029743 units.
d² = 0.51117029743²+0.75974712295-2*0.51117029743*0.75974712295co54
d = 0.61803398875 units.
Therefore, the required angle x is;
(0.61803398875/sin54) = (0.51117029743/sinx)
x = asin(0.66913060636)
x = 42°
