Using a number like 180 directly doesn't let the angle class know if you are referring to degrees or radians. So it doesn't allow directly setting the value, you need to use one of the helper functions that build an angle for you:
sf::Angle angle = sf::degrees(180.0f);
sf::Angle angle2 = sf::radians(3.14f);
view.rotate(sf::degrees(180.0f));
Well you can't use a private constructor ;)
I think it becomes a bit clearer, once we have generated documentation available, since the provided example is relatively clear on the usage:
sf::Angle encapsulates an angle value in a flexible way.
It allows for defining an angle value either as a number
of degrees or radians. It also works the other way
around. You can read an angle value as either a number
of degrees or radians.
By using such a flexible interface, the API doesn't
impose any fixed type or unit for angle values and lets
the user choose their own preferred representation.
Angle values support the usual mathematical operations.
You can add or subtract two angles, multiply or divide
an angle by a number, compare two angles, etc.
sf::Angle a1 = sf::degrees(90);
float radians = a1.asRadians(); // 1.5708f
sf::Angle a2 = sf::radians(3.141592654f);
float degrees = a2.asDegrees(); // 180.0f
using namespace sf::Literals;
sf::Angle a3 = 10_deg; // 10 degrees
sf::Angle a4 = 1.5_deg; // 1.5 degrees
sf::Angle a5 = 1_rad; // 1 radians
sf::Angle a6 = 3.14_rad; // 3.14 radians