Step 1 :Let's denote Angela's old salary as \(old\_salary\) and her new salary as \(new\_salary\).
Step 2 :We know that \(old\_salary = \$42,000\) and \(new\_salary = \$53,000\).
Step 3 :To find out how many times larger Angela's new salary is compared to her old salary, we need to find the ratio of her new salary to her old salary.
Step 4 :This can be done by dividing her new salary by her old salary, which gives us \(ratio = \frac{new\_salary}{old\_salary}\).
Step 5 :Substituting the given values, we get \(ratio = \frac{\$53,000}{\$42,000} = 1.2619047619047619\).
Step 6 :Rounding to two decimal places, we get \(ratio = 1.26\).
Step 7 :Final Answer: Angela's new annual salary is \(\boxed{1.26}\) times as large as her previous annual salary.