If cde is a straight angle, de bisects gdh, m gde = (8x-1), m edh = (6x+15), and m cdf= 43, find each measure.

GDE = 63

EDH = 63

GDH = 126

FDG = 74

FDH = 200

FDE = 137

Step-by-step explanation:

It is stated that DE bisects <GDH. Since bisecting means halving into equal parts, <GDE = <EDH

from the question,

<GDE = (8x-1)

<EDH = (6x+15)

Since <GDE = <EDH,

(8x-1) = (6x+15), if we collect like terms

8x - 6x = 15 + 1

2x = 16

x = 8°

Again, from the diagram, we see that

<GDH = <GDE + <EDH, thus

<GDH = (8x-1) + (6x+15)

<GDH = 8x -1 + 6x + 15

<GDH = 14x + 14, substitute for x

<GDH = 14*7 + 14

<GDH = 112 + 14

<GDH = 126°

<FDG = 180 - <CDF - <GDE

<FDG = 180 - 43 - 63

<FDG = 74°

<FDH = <FDG + <GDE + <EDH

<FDH = <FDG + <GDH

<FDH = 74 + 126

<FDH = 200°

<FDE = <FDG + <GDE

<FDE = 74 + 63

<FDE = 137°

step-by-step explanation: