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Answer :
Final answer:
Given angle KLM = angle KMN, O is the midpoint of KM, OM = 2t + 3, and KN = 8t + 8. The value of t is -5/6.
Explanation:
In the given diagram, we are given that angle KLM is equal to angle KMN, and O is the midpoint of KM.
We are also given that OM = 2t + 3 and KN = 8t + 8.
We need to find the value of t.
Since O is the midpoint of KM, OM = MO. Therefore, we have 2t + 3 = 8t + 8.
By solving this equation, we can find the value of t:
2t + 3 = 8t + 8
Subtracting 2t from both sides:
3 = 6t + 8
Subtracting 8 from both sides:
-5 = 6t
Dividing both sides by 6:
t = -5/6
Therefore, the value of t is -5/6.
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