How To Calculate Angles Between Two Lines

When two non-parallel lines cross, they create an angle between them. If the lines are perpendicular, they form a 90-degree angle. Otherwise, they create an acute, obtuse or other type of angle. Every angle has a "slope." For instance, a ladder against a wall has a slope whose value varies according to the angle of the ladder. Using a little geometry, you can compute the angle between two intersecting lines by determining their slopes.

Step 1

Draw two non-parallel lines on a sheet of graph paper. Label the lines "Line A" and "Line B."

Step 2

Draw a small circle at any point on "Line A." Note its x and y coordinates on the graph paper and call the coordinates x1 and y1. Assume that x1 is 1 and y1 is 2.

Step 3

Draw another small circle at another location on the line. Note the coordinates, and call them x2 and y2. Assume that x2 is 3 and y2 is 4.

Step 4

Write down the following slope equation.

Slope_A = (y2-y1)/(x2-x1)

Plugging in the sample values for the coordinates, you get this equation:

Slope_A = (4-2)/(3-1)

The value for Slope_A is 1 in this example.

Step 5

Repeat these steps and compute the slope of "Line B." Label that slope "SlopeB." For this example, assume that the value for "SlopeB" is 2.

Step 1

Write down the following equation:

TangentofAngle = (SlopeB – SlopeA) / (1+SlopeA*SlopeB)

Step 2

Perform the calculation. The equation looks as follows using the values computed in the previous section:

TangentofAngle = (2-1) / (1+1*2)

In this example, the value for "TangentofAngle" is 0.33.

Step 3

Use the trigonometry table to find the angle whose tangent is "TangentofAngle" as computed previously. If you look up the example value, 0.33, you discover that its corresponding angle, to the nearest 10th of a degree, is 18 degrees. The angle between "Line A" and "Line B" is 18 degrees.