The sum of the measure of angle K and angle J is 180°.

The measure of angle K is 100°.

The measure of angle J is (3x + 5)°.

What is the value of x?

1 answer

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 \(\boxed{25}\).