In the diagram, $\angle A = 30^\circ$, $\overarc{DE} = 170^\circ$, and $\overarc{BC} = 110^\circ$. Find the measure of arc $CE$, in degrees.

In rectangle $ABCD$, we have $AD = 3$ and $AB = 4$. Let $M$ be the midpoint of $\overline{AB}$, and let $X$ be the point such that $MD = MX$, $\angle MDX = 77^\circ$, and $A$ and $X$ lie on opposite sides of $\overline{DM}$. Find $\angle XCD$, in degrees.


Help on this too

It's urgent plz help

I cannot decipher your text on my Mac

- instead of creating the symbols, state them in words
e.g 56 degrees for 56°

in your second question, where is X ?
Is it on some line?

To find the measure of arc $CE$, we need to use the properties of angles and arcs in a circle. Here's how you can do it:

1. Start by noting that angles $\angle A$ and $\angle CED$ are subtended by the same arc, arc $CE$.

2. Since $\angle A = 30^\circ$, we know that arc $CE$ is also $30^\circ$.

3. Now, let's find the measure of arc $DE$. We are given that $\overarc{DE} = 170^\circ$.

4. Note that angles $\angle A$ and $\angle BCD$ are subtended by the same arc, arc $DE$.

5. Since $\overarc{DE} = 170^\circ$, we know that angle $\angle BCD$ is also $170^\circ$.

6. Finally, to find the measure of arc $CE$, we subtract the measure of arc $DE$ from the measure of arc $BC$ (since arc $BC$ is the sum of arcs $DE$ and $CE$).

$CE = BC - DE$

$CE = 110^\circ - 170^\circ$

$CE = -60^\circ$

However, angles and arcs cannot have negative measures, so the actual measure of arc $CE$ is $360^\circ - 60^\circ = 300^\circ$.

Therefore, the measure of arc $CE$ is $300^\circ$.