Angle Basics

Angle Basics


Welcome to introduction to angles
the goal of this video are to know the basic angle vocabulary and also determine how angles are
measured. A portion of a line that starts at A point and continues through B is called Ray. Ray AB can be written using this
notation and angle consists of two rays with a
common endpoint the two rays called the sides at the
angle and the common in point is called the
vertex. So, here we have the vertex. Here we have one side, here we have another
side. There are a couple ways to identify angles. If it call this point A B and C. There’s only one angle at vertex.
But we can simply just call this angle B. However, we can also call this angle ABC. The important part is at the vertex is that variable in the middle. Now, it is true that angle can be formed by two segments with the common endpoint. Each angle has a measure generated by
the rotation about the vertex. The measure is determined by the
rotation of the terminal side about the initial side. So, here’s our initial side and the
second ray or the terminal side has been
rotated this position and when the rotation is
counterclockwise, Its a positive angle. The rotation is clockwise, it’s a
negative angle. The units used to measure are either degrees or radians. We will start by discussing degrees. For degree measure we assign 360 degrees to complete rotation of the Ray you could think of this, that the second
ray going all the way around the circle. Therefore. 1/360th of a
complete rotation gives an angle one degree. Angles can be classified based upon their measure Greek letter theta is often used to
name each angle So just take a look at the
different types of angles if an angle measures between zero in
ninety degrees as we see here it’s called an Acute Angle An angle that equals exactly ninety degrees. is a Right Angle. and then any angle
between ninety and 180. it’s called the Obtuse Angle until we reach
angle of exactly 180 degrees which is a straight angle then any angle between 180 degrees and 360 degrees its called a reflex angle. and then once you reached 360
degrees it’s called a Full angle. Let’s take a moment to see
how we measure angles In trigonometry, we do not spend much time measuring angles. but in geometry you do and the way you
measure angles as with a tool called a Protractor which we see here For example, if we had
an angle here between these two red rays we continue
to measures seventy-three degrees by landing at the initial ray here and measuring from the terminal side. Some protractors have 360 degrees but most only have 180. So, for had anger that was more than 180 degrees we would have to rotate this protractor to find the full
measure of that angle Let’s go and take a look at Complementary and Supplementary angles. If the sum of the measures of two
positive angles is ninety degrees, the angles are called Complimentary. So, in this case we have the measure angle A plus the measure of angle B equals ninety degrees. Now, the sum two angles. Now, the sum of the measures of two positive angles is 180 degrees the angle are called Supplementary. So, in
this case we’ll have to measure of angle A plus the measure of angle B equals 180 degrees. Let’s go and take a look
at a couple examples Two angles are complementary, One angle measures five x degrees while the other measures four x degrees, what is the measure a each angle? so we start with the right angle We’ll divided into two different
angles where one angle is equal to five x degrees, and the others equal to four x degrees for these examples I’ll leave the units
off until the end So, they are complementary we have four x plus five x equals ninety So, we solve this equation
we have nine x equals ninety dividing both sides by nine we can see x is equal to ten So, if this angle is four x or four times ten. Here we have forty degrees and here we would have five time ten or fifty degrees. let’s take a look at one more
example. Now, we have two angles that are
supplementary so they would form 180 degrees and its says here that one
measures seven x degrees and the other one is five x was thirty-six degrees so again the sum of these two angles
were now equal 180 degrees so we have five x
plus thirty-six plus seven x equals 180 so we solve this equation subtract thirty-six on both sides divide by twelve here we have x equals twelve So, if x is twelve, seven times twelve give us eighty-four degrees here and now when I
place X with twelve here, five times twelve plus thirty-six be ninety-six degrees I hope you found this video helpful. Thank you for watching.

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