The other tutor's second angle is incorrect.  It should be 135°.
He thought you wanted the angle between the two radii, not the
angles in standard position.



First we'll find the two points where the line intersects the
circle:



Solve the first equation for x



Substitute in the second equation:







Divide through by 10

Factor

Use zero factor property:
 so 
 so 

To find the x-value correponding to each of those,
substitute each y-value into 

To find the x-value that corresponds to y=1 





Therefore one point of intersecion is (7,1).

To find the x-value that corresponds to y=5 





Therefore the other point of intersection is (5,-5).



We'll take each one separately:
Let's erase everything except the radius on the right:



Let's draw a perpendicular from the point (7,1) to the x-axis,
and label the angle Ꮎ, indicated by the red counterclockwise arc.







That's one answer.   

Now let's erase everything except the radius on the leftt:



Let's draw a perpendicular from the point (7,1) to the x-axis,
and label the angle Ꮎ, indicated by the red counterclockwise arc.






So the reference angle for Ꮎ is 45° degrees.
And it's in the 2nd quadrant so we subtract from 180°
and get 180°-45° = 135°

So the second angle is



Edwin