hey it's Kaeleigh in this lesson we will go over the geometric figure called angles
in more detail ready let's go an angle is made up of two rays whose endpoints
meet at a common point which we call the vertex and we name the angle by using
the letters of the three points on the ankle making sure the vertex point is
always the middle letter so the name of this angle is angle XYZ we measure
angles in degrees when measuring an angle we measure the space between the
two rays we draw an arc to represent the degrees or how much space is between the
Rays when looking at these two angles you can see that the red arc is smaller
than the blue arc that means the angle with the red arc is smaller than the
angle with the blue arc we organized angles by how big their arcs are and
since we measure angles by degrees we organize angles by how many degrees it
has there are four main types of angles right angles are easy to recognize
because we see them all around they make up the corners of doors and
checkerboards when an angle is a right angle we use a
box instead of an arc to tell us how many degrees it is right angles are
always 90 degrees acute angles are angles that are less than 90 degrees
notice the space between the race of this acute angle is less than the space
between the Rays of a right angle acute angles are smaller than right angles a
straight angle is the same as a straight line the arc of a straight line
stretches from ones out of the line to the other it has an
angle of a hundred and eighty degrees an obtuse angle is an angle that is more
than 90 degrees but less than 180 degrees it is right between a right
angle and a straight angle a quick pop quiz can you point to the acute angle
nice and how about the obtuse angle what about the straight angle and where's the
right angle nice work sometimes we have two angles that are
connected here we have angle ABC and angle CBD when this happens they are
called angle pairs there are two special kinds of angle pairs supplementary
angles are an angle pair that is a hundred and eighty degrees when the
angles are added together and they form a straight line here are two different
supplementary pairs for example the red angle has two angles one is 70 degrees
and one is a hundred and ten degrees when these are added together it's a
hundred and eighty degrees the blue angle is made up of two angles both are
90 degrees when these are added together it's a hundred and eighty degrees and
notice that both of these angles form straight lines complementary angles are
a pair of angles whose sum is 90 the red angle pair is made up of two angles both
are 45 degrees when added together the Sun is 90 degrees the blue angle pair is
made up of two angles one is 80 degrees and the other is 10 degrees these are
also complementary angles since their sum is 90 degrees since we know all
about angle pairs we can find the missing angle in these supplementary
angle this one complementary angle this one let's start
with the supplementary angle since we know that this forms a straight line we
know that the sum of the angles is equal to 180 degrees so we can say X degrees
my missing degree plus 35 degrees is equal to 180 degrees now I need to solve
for X here so I will say X is equal to 180 degrees minus with 35 degrees since
I don't know this off the top of my head I'm gonna write it vertically I'm gonna
need to borrow over here so I have 10 minus 5 gives me 5 7 minus 3 gives me 4
and I can bring my 1 down so my missing degree is equal to 145 degrees this one
here is 145 degrees good now let's try the complementary one so since I see
that this here forms a right angle I know that the sum of the angles is 90
degrees so X degrees plus 60 degrees is equal to 90 degrees I solve for my X
here so I subtract 60 from both sides X degrees is equal to 90 degrees minus 60
degrees if you don't know this one you can write it vertically I can think of
it in my head so I know 90 minus 60 gives me 30 degrees so this here is 30
nice so now you get to practice what you've learned about the different types
of angles by doing the online games and quizzes have fun and remember to always
be clever