In the diagram, DG−→− bisects ∠FDH and ∠GDH is complementary to ∠EDF Given ∡FDH =(8x−2)° and ∡EDF =(8x−5)° what is the measure of ∠GDH ?

Answer 1

DG bisects ∠FDH, thus m∠FDG = m∠HDG

m∠HDG = (1/2)m∠FDH

m∠HDG = (1/2)(8x - 2) = 4x - 1

∠GDH is complementary to ∠EDF

m∠GDH + m∠EDF = 90

(4x - 1) + (8x - 5) = 90

12x - 6 = 90

12x = 96

x = 8

m∠GDH = (4x - 1) = 4(8) - 1 = 31