Geometry Find measure

Question

If cde is a straight angle DE bisects angle GDH, GDE=(8x-1), EDH=(6x+15) and angle CDF=43 find each measure x, GDH, FDH, FDE

Answer 1

This question gives you some useful information. CDE is a straight angle - this means these three points are colinear (in a line). Because we are told ray DE bisects the angle GDH, we know that the measures of angles GDE and EDH are equal (definition of bisector). Setting (8x-1)=(6x+15), solve for x (x = 8). Once you have x, you can substitute back into either one of the expressions to find the measure of angles GDE (8(8) - 1 = 63) and EDH; multiply this number by two gives the measure of angle GDH = 2(63)=126.

Although the previous comment about needing to know where F is located to fully answer the question is true, we can still solve some of the angles including F. The angle sum postulate says that CDF + FDE = CDE. We know that CDE is a straight angle (given) and we know angle CDF = 43 (given). A straight angle has the measure of 180. Solving for FDE = CDE - CDF = 180 - 43 = 137

The given information (and missing information) leads to two possible answers for the measure of FDH: (1) If F is located on the same side of the line CE as point G, then angle FDH = FDE + EDH = 137 + 63 = 200. (2) If F is located on the same side of the line CE as point H, the the angle FDH = FDE - EDH = 137 - 63 = 74. Each of these conclusions comes from the angle sum postulate, in one case FDH is the larger angle and in the other, FDE is the larger (sum) of the angles.