Question

What is the measure of angle CED?

Answer 1

Answer:

$m$  

Step-by-step explanation:

we know that

Triangles ABC and CDE are similar triangles, because the corresponding angles are congruent

$m$ ------> by vertical angles

$m$ ----> given problem

$m$ ----> The sum of the internal angles of the triangle must be equal to $180$ degrees

we have

$m$

so

$m$

Answer 2

Angle CED must also measure 60°. 
Because angle m is shown to be congruent to angles ABC and CDE, this means that angle m has a measure of 60 degrees.
There can only be 180 degrees in a triangle, so the measure of angle ACB must be 180-60-60, which equals 60 degrees.
Using the Vertical Angles Theorem, the measure of angle ACB is the same as the measure of angle CED.
Therefore, angle CED measures 60°.