A **s***ecant line* is a line that intersects and passes through a curve or circle at two or more points.

A *tangent line* is a line that intersects a curve or circle at one point.

The point of tangency is the point where the curve or circle intersects the tangent line.

Step 1. The measure of the big arc will be from wx in the picture and the small arc will be from yz

(Big Arc- Small Arc) ⁄ 2

(80°-20°) ⁄ 2

(60°) ⁄ 2 = 30°

Transcript

Hi Welcome to MooMooMath. Today we are going to look at angles created by* secants.* We are looking at *secant sections*. Now a *secant* is a line that through a circle in two places. So we have this line (points to line A Y) is a *secant segment* and A X is a secant segment and we have angle A outside the circle. We need to find the measure of that angle A Now there is a neat little formula that you can learn to find that angle measure. Now what you are doing is looking inside the mouth. Now if this is a mouth we have two arcs. We have a small arc and we have a large arc. If I refer to small arc I’m refereeing to this smaller arc inside the mouth and this larger one (points to top, larger arc.) We are going to take the big arc which is 120 in this case minus the small arc and take the difference and divide by two. So let’s plug in some numbers. The larger arc is 120 the smaller arc is forty. I’m going to subtract those to get 80 and I’m going to divide by two. This angle A is forty degrees. Now this angle is just happened to be the same as the arc. This is not typical so don’t think you just take the arc and stick it down there. You have to subtract and divide by two, but that is how you find the angle. Let’s look at the rules for finding angles created by* secants*. Take the big arc minus the small arc divide by two in order to get the angle measure. Here is a second example of that. We are going to take arc WX the large arc minus YZ the small arc and divide by two. I have replaced WX with 80 minus 20 and divide by two. So take 60 divided by two so angle 1 out here is 30 degrees. Hope this video was helpful

Angle A

Find the measure of the exterior angle A created by two secant lines, if the big arc measures 80 degrees, and the small arc measures 20 degrees.

Step 2. Plug your numbers into the formula and solve

Step 1. Use the formula (Big Arc- Small Arc) ⁄ 2

Step 2. Plug in your numbers (120°-40°) ⁄ 2

Step 3. Solve 80° ⁄ 2 = 40° =Angle A

Angles created by secants explained

When **two secant lines** intersect outside of a circle they form an angle on the exterior of the circle. To find the measure of the exterior angle, you need to know the measure of the two intercepted arcs. Those arcs fall between the two secants. One is large and one is small. To find the exterior angle, use the formula, **big arc - small arc divided by 2. **