Hello
Please attach a couple more pictures-
One taken far enough back to see the whole tree from soil line to top of crown.
One of the trunk showing where it enters the soil.
If there is any visible damage to bark, mushrooms on tree, etc please take a picture of that.

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A little history as well, please: Include how much/how often you water the tree. 
Did you apply any fertilizers or weed killers this season ( within 75-100 feet) ? 
Has there been any construction over the roots?
Do you park vehicles under the tree? Do you store anything heavy on the root zone(lumber, stone,etc?)
Has the area around the tree flooded in the last couple years?
If you have binoculars you could try and follow the wilting branches back toward the trunk, looking for damage like cracked limbs from wind storms or other visual clues like rot, mushrooms growing on the limb.
Sorry for the ‘20 questions’ but, this type information is very helpful to our experts.
I will watch for your update.

We have never needed to water the tree. I did apply a careful squirt of round-up to the leaves of a sumac coming up near its base. No to construction, parking, flooding, & no evidence of cracked limb. It is growing next to a cement pad that was there when it took seed. I can't tell if there are any cracked limbs, but it did receive quite a twist in one of the windstorms we had earlier this year.

We moved to this house in early winter 2017. This tree was a volunteer that I noticed a couple years later. I liked its location, and decided to let it grow.

Hello,
Typically one branch showing signs of drought indicates that something is occurring with that branch. So, you will need to take a close look at the branch all the way down to where it comes off the tree to look for anything abnormal. An injury could cause this. A canker infection from fungus or bacteria can also cause this, although it is uncommon in maples. Look for sunken or otherwise odd looking areas on the branch bark, sap dripping from a lesion, or a tear in the branch bark. 
Finally, could the roundup have drifted to affect the leaves on these two branches? Herbicide injury on tree leaves looks like the leaved are curling, or otherwise disfigured and the leaves become drier each day until they die. 
Without the ability to visit the tree, this is what I can offer. Please do feel free to respond with the results of your inspection. 
Thank you,
-Julie