Based on your givens, you must use your knowledge of opposite angles (opposite angles are equal) and your knowledge of the degree measure of a line (a line is 180 degrees) in order to put together all the clues and solve your problem.The other kind of line and angle problem you may see will involve triangles.You will be presented with a series of givens and then told to find a missing value of some kind.
It can either have termination points (and will be called a “line segment”) or go on infinitely. Parallel lines are two or more lines that are a set distance apart (equidistant) and never meet. Perpendicular lines meet each other at 90 degree angles. The measure of how they meet is expressed in degrees, and the point at which they intersect is called the angle’s “vertex.” Most of what you’ll need to know about lines and angles on the SAT is when and how they will be equal or supplementary to one another.
Equal angles (or lines) are angles (or lines) that have the same measurement.
The missing angles will not always be labeled a, b, c, d, etc.
so the sequence in which to find angles might not be obvious.
That may be difficult to picture, so let’s look at a diagram: (Note: when you are told that two lines are parallel on the SAT math section, the problem will almost always involve opposite interior angles in some way.) Now let’s look at an opposite interior angle SAT problem.
We are told that lines l and m are parallel, so that means the three vertical lines are transversals. The solution to this problem will be slightly different than the solution to the others. There are a couple of different ways you can use this information to determine the measure of angle h. That means that not only are two of the sides equal but two of the angles are also equal. Notice that this triangle gives an angle outside of the triangle.We can see that the angle to the far left is marked as 89 degrees and it is an opposite interior angle to angle r only.This means that r=89 degrees, as opposite interior angles are equal. Almost every line and angle problem is given to you as a diagram problem.Here is one method: Step 1: Determine the measure of the angle adjacent to 148°.The two angles make a straight line and therefore have a sum of 180°.For instance: This is a very typical line and angle problem, so let’s go through it. This means we know that angle b is also 85 degrees because it is opposite f and opposite angles are equal. This means that g must also be 25 degrees because it is opposite angle c.And finally, we know that a line equals 180 degrees.This means that, when we add together angles p and x, their sum will be equal to angle m (because opposite angles are equal). When there are two parallel lines that are crossed by another line (called a transversal), the angles on alternate interiors will be equal to one another.And the angles on the same side of the transversal line and the same side of their respective parallel lines will also be equal.