Given ΔABC, if the exterior angle of A is 68° more than the interior angle of C, the exterior angle of B is 43° more than the interior angle of A, and the exterior angle of C is 25° more than the exterior angle of B. What are the measurements of the interior angles of A, B, and C?
My answer: (Ex means exterior, In means interior)
A = 69 - 111
B = 68 - 112
C = 43 - 137
Ex A - In C = 68
111 - 43 =68
Ex B - In A = 43
112 - 69 = 43
Ex C - Ex B = 25
137 - 112 = 25
I used trial and error but is there a better way to solve this?
Refer to the figure:
The sum of interior angles of triangle is: $$A+B+C=180^\circ \Rightarrow \\ A+[180^\circ-A-43^\circ]+[180^\circ-A-43^\circ-25^\circ]=180^\circ \Rightarrow\\ A=69^\circ, B=68^\circ,C=43^\circ$$