the vertices of the triangle one at (7,4) (1,7) and (-3,-4). find the interior L at the vertex (7,4).

Answer 1

It appears that "interior L" means the interior angle at (7,4)
So, call the three vertices A,B,C and you want angle A.
the slope of AB is -1/2
The slope of AC is 4/5
That makes the angles that AB and AC make with the +x-axis
AB: -26.56°
AC: 38.66°
Thus the angle between AB and AC is 26.56+38.66 = 65.22°

or, we can get the lengths of the sides:
AB = √(3^2+6^2) = √45
AC = √(8^2+10^2) = √164
BC = √(11^2+4^2) = √137
Now the law of cosines says that
a^2 = b^2+c^2 - 2bc cosA
137 = 164 + 45 - 2√7380 cosA
cosA = 6/√205
A = 65.22°