Question

Two parallel lines are cut by a transversal and two of the same-side interior angles formed have measures of (4x+3)° and (x+2)°

Write and solve an equation to find the value of x
Enter the correct answers in the boxes.

Answer 1

To find the value of x for two same-side interior angles formed by a transversal cutting parallel lines, we set up an equation based on the fact that the angles are supplementary. The equation 4x + 3 + x + 2 = 180 simplifies to x = 35 after solving.

Step-by-step explanation:

The student's question involves two parallel lines cut by a transversal, where the same-side interior angles given are (4x+3)° and (x+2)°. To find the value of x, we will use the fact that the same-side interior angles are supplementary, meaning their sum is 180°. We can set up an equation and solve for x:

4x + 3 + x + 2 = 180.

Simplifying the equation, we get:

5x + 5 = 180.

Subtracting 5 from both sides gives us:

5x = 175.

Dividing both sides by 5 gives:

x = 35.

Therefore, the value of x is 35.