Some Important Points Regarding Complementary and Supplementary Angles

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now let us look at some of the facts
with regards to complementary and
supplementary angles so first we will
talk about complementary angles now do
you think that two acute angles can be
complementary no before that
what are acute angles those angles whose
value is less than 90 degrees so angles
measuring less than 90 degrees are
called acute angles so let's say you
have two acute angles so can there be
supplemental that means is it possible
that you add up two angles lesser than
90 degree and the sum would be 90 degree
let us look at these examples it said
this is one angle which is maybe 50
degrees this is another angle which is
40 degrees so when you sum them up it is
90 degree these two together makes 90
degree therefore these two are
definitely complementary so yes two
acute angles can be complimentary let us
look at a few more instances now this is
90 degree right so thickness is a right
angle now let's see if you have two
other sizes wide angle is smaller than
the other their sum is 90 degrees
similarly you might have a situation
like this where this angle is very small
and this angle is quite big but both of
these are acute angles so their sum can
be 90 degrees now there could be a
scenario where this angle is very small
but this angle is quite big and again
the Sun is still 90 degrees so therefore
all of these are complementary angles so
definitely two acute angles can be
complementary now do you think that two
or twos angles can be complementary no
they cannot because what is an obtuse
angle and obtuse ambulance the one whose
measure is greater than 90 degree now we
want the sum to be 90 degree for
complementary angles now if one angle
itself is
90 degrees so there is no chance that it
can add up to some other angle 2 4 90
degree right so two obtuse angles can
never be complementary now do you think
that one acute angle and one or two
samples can be complementary definitely
not that's because again one obtuse
angle itself means greater than 90
degree so you add anything to something
greater than 90 degree so obviously you
are going to give something which is
greater than 90 degree so therefore it
is not at all possible that if either of
the angle is an obtuse angle the sum can
never be 90 degree and therefore an
obtuse angle can never be part of
complementary angles so obtuse angle
would be something like this which in
itself is greater than 90 degree
therefore they can never be
complementary
so let's see this little plug meeting an
example let's say the value of this
angle is 120 degree which is obtuse
angle and the value of this one is 30
degree which is actually dangle so when
you try to find the sum sum would be 120
plus 30 which is 150 degree so do you
think it is 90 no and it is actually not
feasible because one value is itself
greater than 90 so how can the Sun be
equal to 90 so obvious and then cannot
be complimented two right angles cannot
be complementary again because one right
angle one right angle means how much one
right angle is exactly equal to 90
degree so in order to in order that this
right angle is compliment of some other
angle the other angle has to be zero
Degree which is actually nothing
therefore two right angles cannot be
complementary again now let us look at
some similar facts on supplementary
angles so let us quickly look at the
facts with regards to supplementary
angles now do you think that two acute
angles
be supplementary no never why that's
because both of these angles and less
than 90 degrees now let's take an
example let us say that you have two
acute angles maybe one angle is
somewhere around 45 beginning and let's
see the other hand is 70 degrees
so let's assume these are the angles
that you have so what would be the Sun
so the Sun would be 70 plus 45 which
would be 115 so do you think this is
this is equal to 180 degrees
no so basically you think of any acute
angles let's try to think of the maximum
possible acute angle maybe something
like 89 degrees so even if you have two
89 degrees just add them up how much do
you get you get 178 degrees which is
still less than 180 degrees therefore
supplementary angles cannot be formed by
two acute angles two obtuse angles
cannot be supplementary again now that's
because then you consider two obtuse
angles now each of us angle is greater
than 90 degree now when you add two
obtuse angles then the sum becomes
greater than 180 degree so with two
obtuse angles sum becomes greater than
180 degree with two acute angles the sum
is less than 180 degrees so because of
these even neither two acute angles nor
two obtuse angles can be supplemented so
this should be supplemental however one
acute and one obtuse angles can
definitely be supplementary so this is a
typo so there should be supplementary so
if you take one acute angle and one
obtuse angle then that can be a perfect
supplementary angles let us have a
look at some examples so let's look at
this one so let's say that this Apple
now this is definitely supplementary
angles because the sum of these two
angles is definitely 180 degree which is
a straight line right so here when you
look at this angle this is obvious it is
greater than 90 degree right 90 degree
would have been something like this this
would have been actively so it is
greater than 90 so this is obtuse and
this one is a cube because it is less
than 90 so one obtuse one acute make a
perfect supplement there similarly if
even if you think it in this way let's
say that you have something like this
instead of this if you have two right
angles this is also 90 and this is also
90 so both of these are right angles so
do you think they make a supplementary
pair yes definitely so here also this is
talking about supplementary so two right
angles is always supplement because 90
degree plus 90 degree forms a 180 degree
so basically two right angles will
always be supplementary here so these
we're a couple of things with regards to
complementary and supplementary angles
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