Mathematics Question and Solution
Let AB be 1 unit.
a² = 2-2cos108
a = 1.61803398875 units.
a is BE.
(1.61803398875/sin156) = (b/sin6)
b = 0.41582338164 units.
b is BP.
(1.61803398875/sin156) = (c/sin18)
c = 1.22929666779 units.
c is EP.
d = 72-18
d = 54°
e² = 1+0.41582338164-2*0.41582338164cos54
e = 0.82709091528 units.
e is CP.
(0.82709091528/sin54) = (1/sinf)
f = 78°
Notice;
f is the supplementary angle of angle BPC.
f' = 180-f
f' = 180-78
f' = 102°
f' is angle BPC.
g = 72-8
g = 66°
g is angle DEP.
h² = 1+1.22929666779²-2*1.22929666779cos66
h = 1.22929666779 units.
h is DP.
Notice;
DP = EP
Therefore;
Angle DEP = Angle PDE = 66°
Angle DPE is;
180-2*66
= 180-132
= 48°
Therefore the required angles, x and y are;
x = 360-156-102-48
x = 54°
y = 66-36
y = 30°
