Question

How to find a angle measure with the Pythagorean theorem?

Answer 1

The Pythagorean Theorem states that: "the sum of the squares of the legs is equal to the square of the hypotenuse." 
a² + b² = c² or  c² = a² + b²

Note¹: Hypotenuse is the side opposite the right angle.
Note²: The legs are the sides that are not opposite the right angle.

Examples: (Use the attachments for better understanding:)

*First example
$x^2 = 9^2 + 12^2$
$x^2 = 81 + 144$
$x^2 = 225$
$x = \sqrt{225}$
$\boxed{x = 15}\end{array}}\qquad\quad\checkmark$

Second example:
$x^2 = 10^2 + 40^2$
$x^2 = 100 + 1600$
$x^2 = 1700$
$x = \sqrt{1700}$
$\boxed{x \approx 41.23}\end{array}}\qquad\quad\checkmark$