Question

What is the value of x?
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X =??

Answer 1

x = 9

Explanation:

Triangles are similar due to AAA (all angles are congruent due to shared angle and corresponding angles). Thus, the sides are proportional, and we can set up a proportion with corresponding sides:

9/(72 + 9) = (3x - 20)/(3x - 20 + 56)

9/81 = (3x - 20)/(3x + 36)

(1/9) * (3x + 36) = 3x - 20

(3x + 36)/9 = 3x - 20

3x + 36 = (3x - 20)*9

3x + 36 = 27x - 180

36 + 180 = 27x - 3x

216 = 24x

x = 9