What is the measure of jhn?

25°
45°
50°
95°

The measure of ∠JHN is 45° .

Step-by-step explanation:

As the figure is given in the question .

∠LHK = ∠MHJ

(Vertically opposite angles)

Let us assume that

∠LHK = ∠MHJ = y °

Thus

∠LHK + ∠KHN + ∠JHN = 180°

(These angles are supplementary angles.)

As ∠KHN= (x + 25)°

∠JHN = (x + 20)°

∠LHK = y °

Putting in the above

y° +  (x + 25)° +  (x + 20)° = 180°

y + x + 25 + x + 20 = 180

y + 2x = 180 - 45

y + 2x = 135

Now

∠LHM + ∠MHJ= 180°

(These angles are supplementary angles.)

∠MHJ = y °

∠LHM = (3x + 20)°

Putting in the above

y° + (3x + 20)° = 180°

y + 3x = 160

Two equations becomes

y + 2x = 135

y + 3x = 160

Subtracted  y + 2x = 135 from y + 3x = 160 .

y - y + 3x - 2x = 160 -135

x = 25

Thus

∠JHN = (x + 20)°

          = (25 + 20)°

          = 45°

Therefore the measure of ∠JHN is 45° .

the value of x is 28.2