Exterior Angles Triangle Finding the Unknown Angle - Triangle & its Properties Video Lecture - Class 7

welcome today we're going to look at
exterior angles of triangles and the
first thing we're going to do is review
some of the rules that we already know
the first one is that we have a straight
line and we've divided it into two the
sum of those angles equals 180 degrees 0
I've a line divided into 2 and so D plus
C equals 180 degrees the second thing we
know is that the interior angles and by
that I mean the angles inside the
triangle they also add up to 180 degrees
so here event triangle and angles a plus
B plus C equal 180 degrees these are
going to come in useful later on when we
work out exterior angles but first let's
have a look at what I mean when I say an
exterior angle so I have a triangle and
if I extend one of the sides outwards
the angle that's formed with this line
to the triangle is what I mean when I
say an exterior angle so for our
definition it can be an exterior angle
of a triangle is formed when any side is
extended outwards so rather than the
angles inside the triangle an exterior
angle is outside the triangle so now
that we have our rules and we have a
definition we can come up with another
rule for exterior angles themselves so
again we have a triangle we've extended
one of the sides outward and this is
what we know is our exterior angle so
let's enable the rest of the triangle
with some useful information so the top
let's put angle a on the left hand side
let's put angle B and on the right hand
side let's put angle C at the sake of
argument let's call exterior angle angle
D so given this information what we can
do is come up with a way of working out
our exterior angles so the first thing
that we can notice is the angle CLD
there on the straight line so adding
those together will equal 180 degrees so
D plus C equals 180 degrees then the
next thing that we can notice is that
inside the triangle these angles will
also add up to 180 degrees so a plus B
plus C equals 180 degrees but now that
we have these we have two rules instead
of one so we're going
look at trying to combine this
information so here's a simple algebra
on the left-hand side we are going to
try and put the C onto the side with the
180 degrees so in order to do that what
I have to do is change the sign of the C
from a positive to a negative because
I've taken it over the equal sign so I
get D equals 180 degrees minus C I do
exactly the same thing on this side so I
get a plus B equals 180 degrees minus C
so now what I can notice is that both
equations actually equal the same thing
which is 180 degrees minus C so using
some simple substitution I can simply
write D equals a plus B now if I have
the angle C I can simply plug the
information into this equation here but
most often in textbooks they don't give
us the angle C so we have to come up
with some other way of finding out the
information so our exterior angle here D
is equal to the sum of the opposite
interior angles and in this case that's
a plus B so D equals a plus B so let's
have a look at an example of an exterior
angle so this is a question which is
quite often posts and some textbooks
evaluate which just means work out
so evaluate triangle ABC where a is 40
degrees and B is 60 degrees what is the
exterior angle to a CB so we know that
the exterior angle is going to be here
so we want to work out angle D so if we
draw that triangle what we can do is
replace a with 40 degrees B with 60
degrees and we know that the angles
going to come out here because it's a CB
so this is going to be the exterior
angle that we're going to try work out
so here what we can do is write down our
rule which is d equals a plus B replace
a with 40 and B with 60 and we get D
equals 100 degrees simply by adding
those two values together so now I think
it's your turn so I'm going to put a
question here and what I suggest you do
is pause the video
one will come back we'll walk through it
together welcome back hopefully what
you've done is draw a triangle because
sometimes that helps put things into
perspective so this is my drawing of the
question above and I've written D equals
a plus B replacing a with 50 and B were
30 I get 80 degrees so let's have a look
at example 2 and again I suggest you
pause the video and when we come back
we'll look at this together what we
should have done is draw a triangle if
you didn't do that in the first example
hopefully you managed to do that in the
second and again we've got our Rule D
equals a plus B and then we looked
replacing a with 90 degrees and B with
40 degrees we get D equals 130 degrees
hopefully you got those both right well
done if you did and hopefully that will
now explain exterior angles for you take
care