Mathematics Question and Solution
Let the two equal lengths, AB and CD be 1 unit.
a = 180-50-15
a = 115°
a is angle ADB.
b = 180-a
b = 65°
b is angle ADC.
(1/sin115) = (c/sin50)
c = 0.8452365235 units.
c is AD.
d² = 0.8452365235²+1²-2*0.8452365235cos65
d = 1 unit.
d is AC.
It implies, triangle ACD is isosceles.
Therefore, the required angle theta, let it be e is;
e+2b = 180
e+2(65) = 180
e = 190-130
e = 50°
e is the regular angle, theta, angle ACB.
Notice!
Triangle ABC is isosceles.
