How do i find the value of x and measure of angle ebd?

Use the congruence statement to determine that ∠ABF = 5x°. Then, add ∠EBF to ∠FBA to get ∠EBA = 10x°.

Now, remove segment BF and it's easy to see that ∠EBA and ∠CBD are vertical angles, hence equal to each other. This gives you a relationship that lets you find the value of x and the values of all the angles.

... 10x = 2x +84 . . . . vertical angles are equal

... 8x = 84 . . . . . . . . subtract 2x

... x = 10.5 . . . . . . . . . divide by 8

∠EBD is the supplement to ∠CBD, which is 10x° = 105°.

... ∠EBD = 180° -105° = 75°

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.

if im not mistaking its

step-by-step explanation: