WILL MEDAL Given Angle 1 = Angle 2, Find X

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WILL MEDAL Given Angle 1 = Angle 2, Find X

Geometry
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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1 Attachment
Do you know the triangle angle bisector theorem?
The bisector of an angle pf a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the adjacent sides.

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|dw:1435254823038:dw|
In the triangle of the above figure, if angles 1 and 2 are congruent, then a/b = c/d
In your case you have \( \dfrac{3}{x - 4} = \dfrac{x}{4} \)
Now solve the proportion for x.
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6 or -2
@Falling_In_Katt You solved the proportion correctly. The solutions to the equation are 6 and -2. In this problem, x represents a length. A length can't be negative, so discard the negative solution, -2, and keep only the positive solution 6.

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