Respuesta :

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ANSWER:

x = 5

The value of ( x ) is equivalent to 5.

STEP-BY-STEP 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
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