Complementary, Supplementary & Vertical Angles – Geometry

Complementary, Supplementary & Vertical Angles – Geometry


When you first learn about angles you learn forwards about angles of different sizes acute, right, obtuse and Straight Angles These terms all describe a single angle, but there are also terms that 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 [and] d the 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 You’d say this fact more simply as vertical Angles are equal let’s 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] Whenever two Angles add up to 180 degrees. We call them supplementary angles The reason there’s a name for this special case is because in geometry and trigonometry you’ll encounter this situation a lot Do note that two Angles don’t have to be next to each other to be supplementary For example these two angles are supplementary because their sum 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 plus b plus 90 degrees equals 180 degrees if You subtract 90 degrees from both sides you [get] 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 to 90 degrees complementary Angles Here’s the way to remember the difference between complementary and supplementary Angles When somebody says [something] and you totally agree [with] them you might say you’re right It’s kind of a compliment and two complimentary Angles form a right angle Let’s see an example what is the size of the 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 two [Angles] are complementary What is the size of Angle B? well if two angles are complementary then their sum is 90 degrees, so 35 degrees plus B equals 90 degrees if you solve for b. You get b equals 55 degrees

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