Question

find the value of x in the diagram above

Answer 1

Given that :-
AB = BD = CD

So,
Angle DCB = Angle DBC (Angles opposite to equal sides of a triangle are equal)
So,

Angle DBC = x

Now,

AB = BD

So,
Angle BAD = Angle BDA (Angles opposite to equal sides of the triangle are equal ). .... (1)

Now ,
Exterior angle DBC = BAD + BDA
Or,
2BAD = x (since, DBC = x and from (1)
Or,
BAD = x / 2

Now ,

Exterior Angle ADE = ACD +DAC
Or,
$x + \frac{x}{2} = 75 \\ \\ \frac{3x}{2} = 75 \\ \\ 3x = 75 \times 2 = 150 \\ \\ x = \frac{150}{3} = 50$

So,
X is equal to 50°


Please refer the above photograph for the figure and naming.

Thanks!