Respuesta :

Answer:

x = 3

AB = 18

Step-by-step explanation:

Based on the midsegment theorem:

[tex] MN = \frac{1}{2}(AB) [/tex]

MN = 9

AB = x + 15

Plug in the values and solve for x

[tex] 9 = \frac{1}{2}(x + 15) [/tex]

Multiply both sides by 2

[tex] 9 \times 2 = \frac{1}{2}(x + 15) \times 2 [/tex]

[tex] 18 = x + 15 [/tex]

Subtract 15 from each side

[tex] 18 - 15 = x + 15 - 15 [/tex]

[tex] 3 = x [/tex]

x = 3

AB = x + 15

Plug in the value of x

AB = 3 + 15

AB = 18

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