ANSWER:
x = 5
The value of ( x ) is equivalent to 5.
Explanation:
Testing triangle AHD is congruent to triangle CHD -
Angle ADH = Angle CDH ( given )
Side AH = Side CH ( given )
Angle AHD = Angle BHC = 90° ( equal vertically opposite angles )
Angle CHD = 180° - Angle AHD = 180° - 90° = 90° ( supplementary angles on a straight line )
Angle AHD = Angle CHD = 90°
Angle DAH = Angle DCH ( angle sum of a triangle )
Therefore, triangle AHD is congruent to triangle CHD.
As triangle AHD is congruent to triangle CHD, we can do the following:
AD = 2x - 3
CD = x + 2
AD = CD
THEREFORE:
2x - 3 = x + 2
2x - x = 2 + 3
x = 5