degree, decree

Degree or degree means a step in a series or scale--
He became a 12th degree mason recently.
"To the nth degree" means to the very limit.
Degree also means extent, scope, or level--
They reached a degree of consensus that everyone could live with.

Degree also means a measurement of the distance around a circle or arc, or the width of an angle--
There are 360 degrees in a circle.
Degree is also a measure of temperature--
It hasn't warmed up by even one degree.
It's so hot out.It must be at least 90 degrees.
It's so cold out.It must be ten degrees below zero.

Degree is also what someone earns in college--
He was granted his degree in physics.

 Decree means a public proclamation--
"There went out a decree from Caesar Augustus that all the world should be taxed."
 According to the new decree, everyone must be indoors by 9 pm.

Now that you know that you can say--
"They reached a degree of acceptance of the new decree."

Note--"to a degree" means to a certain extent--
I believe what the speaker said, to a degree.
"They agree, to a degree" means they agreed, but not about all of the points or particulars.
"By degrees" means in steps or stages--
They got used to the new method by degrees.