Mathematics Question and Solution
Let the two congruent lengths be 1 unit.
(1/sin50) = (a/sin80)
a = 1.28557521937 units.
(1.28557521937/sin110) = (b/sin60)
b = 0.46791111376 units.
(1/sin70) = (c/sin80)
c = 1.04801052092 units.
sin60 = d/2
d = √(3) units.
e = d-c
e = √(3)-1.04801052092
e = 0.68404028665 units.
f² = 0.68404028665²+0.46791111376²-2*0.68404028665*0.46791111376cos70
f = 0.68404028665 units.
Notice;
e = f
Therefore the required angle x, is;
180-2*70
= 180-140
= 40°
