A side of the triangle below has been extended to form an exterior angle of 144°. Find the value of xx.

Answer 1

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]

Answer 2

A side of the triangle below has been extended to form an exterior angle of 144°. Find the value of x.

Answer 3

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 $x=36^\circ - 77^\circ = \boxed{-41}.$