∠dhg= 4x+12 and ∠bgh=8x-24. find the measure of ∠dhg

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°

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.