Questions: What is the value of (x) ?

What is the value of (x) ?
Transcript text: What is the value of $x$ ?
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Solution

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Solution Steps

Step 1: Identify the angles in the triangle

The given triangle \( \triangle LMN \) has the following angles:

  • \( \angle L = (6x - 4)^\circ \)
  • \( \angle M = (10x + 1)^\circ \)
  • \( \angle N = 77^\circ \)
Step 2: Use the triangle angle sum property

The sum of the angles in a triangle is always \( 180^\circ \). Therefore, we can write the equation: \[ (6x - 4) + (10x + 1) + 77 = 180 \]

Step 3: Simplify the equation

Combine like terms: \[ 6x - 4 + 10x + 1 + 77 = 180 \] \[ 16x + 74 = 180 \]

Step 4: Solve for \( x \)

Subtract 74 from both sides: \[ 16x = 106 \] Divide by 16: \[ x = \frac{106}{16} \] \[ x = 6.625 \]

Final Answer

The value of \( x \) is approximately \( 6.625 \). However, since the given options are 5, 7, 26, and 51, none of these options are correct based on the calculation.

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