Questions: In triangle KLM, m angle K=(2x+4)°, m angle L=(2x+14)°, and m angle M=(10x+8)°. What is the value of x?

Transcript text: In $\triangle$ KLM, $\mathrm{m} \angle K=(2 x+4)^{\circ}, \mathrm{m} \angle L=(2 x+14)^{\circ}$, and $\mathrm{m} \angle M=(10 x+8)^{\circ}$. What is the value of $x$ ?

Solution

Solution Steps

Step 1: Set Up the Equation

We know that the sum of the angles in triangle $ KLM $ is $ 180^\circ $. Therefore, we can write the equation: \[ (2x + 4) + (2x + 14) + (10x + 8) = 180 \]

Step 2: Simplify the Equation

Combining like terms, we simplify the left side of the equation: \[ 2x + 4 + 2x + 14 + 10x + 8 = 180 \] This simplifies to: \[ 14x + 26 = 180 \]

Step 3: Solve for $ x $

Next, we isolate $ x $ by first subtracting $ 26 $ from both sides: \[ 14x = 180 - 26 \] This gives us: \[ 14x = 154 \] Now, we divide both sides by $ 14 $: \[ x = \frac{154}{14} \] Simplifying this fraction results in: \[ x = 11 \]

Final Answer

$\boxed{x = 11}$

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