Mathematics Question and Solution
Let the base of the quadrilateral be 1 unit.
a = 180-58-28-38
a = 180-124
a = 56°
(1/sin56) = (b/sin(58+28))
b = 1.2032796622 units.
(1/sin56) = (c/sin38)
c = 0.7426219217 units.
d = 180-72-46
d = 180-118
d = 62°
(1.2032796622/sin62) = (e/sin46)
e = 0.9803152067 units.
f = 180-28-38-46
f = 180-112
f = 68°
(1/sin68) = (g/sin(38+46))
g = 1.0726264165 units.
h = 180-78-58
h = 44°
(1.0726264165/sin44) = (j/sin78)
j = 1.5103639435 units.
k = j-c
k = 0.7677420218 units.
l = 180-56-72
l = 180-128
l = 52°
m² = 0.7677420218²+0.9803152067²-2*0.9803152067*0.7677420218cos52
m = 0.7897570103 units.
Therefore, the required angle, x is;
(0.7897570103/sin52) = (0.7677420218/sinx)
x = 50°
