<h3>Answer: Choice B) 8.57</h3>
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Explanation:
The triangles are similar through the AA (angle angle) similarity rule. Note how the angle markers correspond and match up. Example: angle C and angle F both have triple angle markers to indicate these angles are congruent.
The corresponding sides pair up to form equal fractions. AB and DE form AB/DE which is equal to AC/DF, as these two sides correspond as well.
Therefore: AB/DE = AC/DF
Let's plug in the given values and isolate x
AB/DE = AC/DF
11/7 = (15+x)/15 ...... substitution
11*15 = 7*(15+x) ....... cross multiply
11*15 = 7*15+7*x ...... distribute
165 = 105+7x
165-105 = 105+7x-105 ..... subtract 105 from both sides
60 = 7x
7x = 60
7x/7 = 60/7 ............ divide both sides by 7
x = 8.57142857142858
x = 8.57 ..... rounding to the nearest hundredth
