Answer:
The measure of ∠JHN is 45° .
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° .