f CDE is a straight angle, DE bisects GDH, m GDE = (8x 1) ° , m EDH = (6x + 15) ° , and m CDF = 43 ° , find each measure.

Answer 1

From the way the problem is worded:

CDE is a straight angle made up of three angles: CDF of measure 43, FDG of unknown measure and GDE of measure 8x + 1.

EDH is outside CDE and is of measure 6x + 15.

Since DE bisects GDH to form GDE and EDH, those latter two angles are equal and thus 8x + 1 = 6x + 15 and x = 7 and substituting 7 for x, both angles are equal to 57 degrees.

Since CDF is 43 and GDE is 57 and CDE is 180 in total, then FDG = 180 - 43 - 57 = 80 degrees.