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 △LMN \triangle LMN has the following angles:

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

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

Step 3: Simplify the equation

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

Step 4: Solve for x x

Subtract 74 from both sides: 16x=106 16x = 106 Divide by 16: x=10616 x = \frac{106}{16} x=6.625 x = 6.625

Final Answer

The value of x x is approximately 6.625 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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