Answer:
1. AD and BD are congruent.
Therefore,
[tex]3x - 4 = 2x + 5\\3x - 2x = 5 + 4\\x = 9[/tex]
To get the value of AD, substitute x with 9.
[tex]3(9) - 4 = 23\\2(9) + 5 = 23[/tex]
Since BD is congruent to AD, the value is the same. Therefore, both line BD and AD are equal to 23.
2. Angle A and B are also congruent.
Therefore,
[tex]5x = x + 12\\5x - x = 12\\4x = 12\\\frac{4x}{4} = \frac{12}{4}\\x = 3[/tex]
Verify:
[tex]5(3) = (3) + 12\\15 = 15[/tex]
