When you first learn about angles, you learn forwards about angles of different sizes and acute. Obtuse and Straight Angles, Vertical Angles
Vertical Angles Definition:
The vertical angle is created by two adjacent straight lines intersecting at a non-adjacent angle. Two straight lines form an “X” by being positioned across from each other at the corners. These are often referred to as vertically opposite angles as they are positioned opposite one another.
These terms all describe a single angle, but some words describe pairs of angles. These are vertical. Supplementary and complementary angles
Suppose two lines cross one another. There are now four angles. Let’s give them names A, B, C, D. Angles opposite one another are the same, so A and [C] are the same size, and B and [D] are equal?
We call angles across from one another vertical angles. Focus on the top half for a moment. These two angles form a straight angle A. 180-degree angle. This means that a plus b equals 180 degrees. Two angles added together equal 180 degrees.
There’s a name for this special case because, in geometry and trigonometry, you’ll encounter this situation a lot. It is important to note that two angles need not be adjacent to be supplementary. The sum of these two angles, for example, is 180 degrees.
Next, let’s look at a right triangle. This angle measures 90 degrees. Let’s call the other two angles A and B. Since the sum of the angles of any triangle equals 180 [degrees], we have A + B plus 90 degrees equals
Vertical angles equal
180 degrees subtract 90 degrees from both sides A plus B. Equals 90 degrees
Because right triangles are so common in geometry and trigonometry, there’s a term for two angles that add up to 90 degrees.
Complementary Angles: Here’s the way to remember the difference between complementary and supplementary Angles. Two complementary angles form an effective right angle.
vertical angles examples
What is the size of angle A?
These two angles are supplementary, so a plus 65 degrees equals 180 degrees. If you subtract 65 from both sides, you get a equals 115 degrees. Let’s see another example. Suppose these angles are complementary.
What is the size of Angle B?
If two angles are complementary, their sum is 90 degrees, so 35 degrees plus B equals 90 degrees if you solve for b. You get b equals 55 degrees