Applying the angle bisector theorem, the value of x is: B. 5.3.
What is the Angle Bisector Theorem?
An angle bisector divides an angle into two congruent halves. According to the angle bisector theorem, an angle bisector of a triangle divides the interior angles opposite sides in such a way that the corresponding lengths are proportional to each other. This means that the corresponding sides have ratios that are equal.
How to Apply the Angle Bisector Theorem to Find x?
In the image given, applying the angle bisector theorem, we have the following proportion which we can use to find the value of x in the triangle given above:
6/x = 9/8 [according to the angle bisector theorem]
Cross multiply
(9)(x) = (6)(8)
9x = 48
Divide both sides by 9
9x/9 = 48/9
x = 5.333
Thus, to the nearest tenth, the value of x is approximately calculated as: B. 5.3
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