Which of the following is a properly punctuated complex sentence?

After Betty got tired of teaching yoga, she started a new career making bowls and dishes out of clay.
Betty got tired of teaching yoga and she started a new career making bowls and dishes out of clay.
Betty got tired of teaching yoga; she started a new career making bowls and dishes out of clay.
Betty started a new career making bowls and dishes out of clay after getting tired of teaching yoga

Betty started a new career making bowls and dishes out of clay after getting tired of teaching yoga.

The properly punctuated complex sentence is: "Betty started a new career making bowls and dishes out of clay after getting tired of teaching yoga."

To determine which of the following is a properly punctuated complex sentence, let's first understand what a complex sentence is. A complex sentence is made up of an independent clause and at least one dependent clause. An independent clause can stand alone as a complete sentence, while a dependent clause cannot.

Now, let's analyze the given options:
1. After Betty got tired of teaching yoga, she started a new career making bowls and dishes out of clay.
This option is a properly punctuated complex sentence. The independent clause is "she started a new career making bowls and dishes out of clay," and the dependent clause is "After Betty got tired of teaching yoga."

2. Betty got tired of teaching yoga and she started a new career making bowls and dishes out of clay.
This option is not a complex sentence as it consists of two independent clauses joined by a coordinating conjunction "and". To make it a complex sentence, you would need to add a dependent clause.

3. Betty got tired of teaching yoga; she started a new career making bowls and dishes out of clay.
This option is not a complex sentence either. Although it uses a semicolon correctly to separate two related independent clauses, the second clause is still not dependent on the first one.

4. Betty started a new career making bowls and dishes out of clay after getting tired of teaching yoga.
This option is also a properly punctuated complex sentence. The independent clause is "Betty started a new career making bowls and dishes out of clay," and the dependent clause is "after getting tired of teaching yoga."

Therefore, the first option, "After Betty got tired of teaching yoga, she started a new career making bowls and dishes out of clay," is the properly punctuated complex sentence.