What is the value of x? enter your answer in the box

see the attached figure with letters to better understand the problem

we know that

m∠BCA=m∠ECD ----------> by vertical angles

m∠BAC=m∠CED --------> given problem

we know that

If two triangles have two identical internal angles, then the triangles are similar.

so

Triangles ABC and EDC are similar

by proportion

therefore

the answer is

the value of x is

add an image

step-by-step explanation:

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).