A side of the triangle below has been extended to form an exterior angle of 144°. Find the value of xx.
Since the exterior angle of a triangle is equal to the sum of the two remote interior angles, we know that $x + 77 = 144.$ Solving this equation yields $x = \boxed{67}.$
[asy]
unitsize(1inch);
pair A,B,C;
A=(0,0);
B=(13,0);
C=(5,12);
draw(A--B--C--cycle, black+linewidth(1));
label("$x^\circ$",B,(0,-2));
label("$x+77^\circ$",C, (2,3));
draw(C--(15,0));
[/asy]
A side of the triangle below has been extended to form an exterior angle of 144°. Find the value of x.
Since the exterior angle of a triangle is equal to the sum of the two remote interior angles, we have $x+77 = 180^\circ - 144^\circ.$ Simplifying the right side gives $x+77 = 36^\circ.$ Subtracting 77 from both sides gives $x=36^\circ - 77^\circ = \boxed{-41}.$
To find the value of xx, we need to use the fact that the sum of the measures of an exterior angle and its corresponding interior angle is always 180 degrees.
Let's denote the interior angle corresponding to xx as A. Since the exterior angle is 144 degrees, we can write:
A + 144 = 180
To solve for A, we subtract 144 from both sides of the equation:
A = 180 - 144
A = 36 degrees
Therefore, the value of xx is 36 degrees.