Atriangle is defined by the three points: a=(5,10) b=(10,7) c=(4,5). determine all three angles in the triangle (in radians

The slopes of the line segments and the angle each makes with the x-axis are
.. ab, -3/5, -0.5404195 rad
.. bc, 1/3, 0.3217506 rad
.. ca, 5, 1.3734008 rad

Then angle a is -0.5404195 -(1.3734008 -π) ≈ 1.22777 rad
Angle b is 0.3217506 -(-0.5404195) ≈ 0.86217 rad
Angle c is 1.3734008 -0.3217506 ≈ 1.05165 rad

Check:
The sum of the angles should be π.
.. 1.22777 +0.86217 +1.05165 = 3.14159 . . . . accurate to 5 dp