Question

An angle measurement has parallel lines, L1 and L2, running across. A line, t, goes through those two lines at an angle. Same side interior angles, (2x + 20) degrees and (3x - 10) degrees, lie on the interiors. What is the angle measurement?

Answer 1

To determine the angles formed by a transversal cutting through two parallel lines, we solve for x using the property that same side interior angles are supplementary. Solving the equations (2x + 20) + (3x - 10) = 180 yields x = 34 degrees. With that, we can find the individual angle measures to be 88 degrees and 92 degrees.

Step-by-step explanation:

To find the angle measurement when we have parallel lines L1 and L2 and a transversal t, we use the relationship between the same side interior angles. According to the properties of parallel lines cut by a transversal, same side interior angles are supplementary, meaning that their sum is 180 degrees.

To solve for x in the given same side interior angles, (2x + 20) degrees and (3x - 10) degrees, we set up the equation:

• (2x + 20) + (3x - 10) = 180

Combining like terms, we have:

• 5x + 10 = 180

Subtracting 10 from both sides, we get:

• 5x = 170

Dividing both sides by 5 gives us:

• x = 34 degrees

Finally, to find the individual angle measurements, we substitute x back into the expressions for the angles:

• (2x + 20) degrees = (2(34) + 20) degrees = 88 degrees
• (3x - 10) degrees = (3(34) - 10) degrees = 92 degrees

Which confirms that both angle measurements add up to 180 degrees as expected for same side interior angles on parallel lines intersected by a transversal.