Question

∠DHG= 4x+12 and ∠BGH=8x-24. Find the measure of ∠DHG

Answer 1

by property of parallel lines (lines DH and BG are parallel):

∠DHG = 180° - ∠BGH  [∵ corresponding angles are equal]

⇒ 4x + 12 = 180 - (8x - 24)

⇒ 12x -12 = 180

⇒ 12x = 192

∴ x = 16

now substituting this value of x in ∠DHG:

4 × 16 + 12 = 76°