We know that the sum of the measures of angle K and angle J is 180°. We can express this as the equation:
\[ \text{Measure of angle K} + \text{Measure of angle J} = 180° \]
Given that:
- The measure of angle K is \(100°\)
- The measure of angle J is \((3x + 5)°\)
We can substitute these values into the equation:
\[ 100° + (3x + 5)° = 180° \]
Now, we can simplify the equation by combining the constant terms:
\[ 100 + 3x + 5 = 180 \]
This simplifies to:
\[ 105 + 3x = 180 \]
Next, we will isolate \(3x\) by subtracting \(105\) from both sides:
\[ 3x = 180 - 105 \]
Calculating the right side gives us:
\[ 3x = 75 \]
Now, we divide both sides by \(3\) to solve for \(x\):
\[ x = \frac{75}{3} \]
This simplifies to:
\[ x = 25 \]
Thus, the value of \(x\) is \(\boxed{25}\).
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