Solved Examples On Complementary Angles - Lines & Angles Video Lecture - Class 7

ok so let us solve a few examples on the
complementary angles before we move on
to the discussion of supplementary
angles so let's look at the question
what is the measure of compliments of
each of the following angles and we have
four angles that is ABC HD and we have
to find out the complement of this angle
now let me just reiterate the criteria
for two angles to be complement of each
other is when their sons that is angle x
plus angle Y let us say that these are
these there are these two angles when
the measure of these two angles the sum
of measure of these two is equal to 90
degrees then they are known as
complementary angles
having said that let us look at the
examples here so we have first one which
says that angle let's say that we have
angle X in all the cases this is all
English and you have to find out angle Y
so in problem a we have angle X plus
angle y equals 90 degrees so we know
that angle X is equal to 45 degrees
right so 45 degrees plus and y equals 90
degrees we can transpose this 45 degrees
to the other side right it is the same
as subtracting 45 from both the sides so
we get tangled y equals 90 degrees minus
45 degrees which gives us angle y equals
45 degrees so the supplementary and are
the complementary angle of 45 degrees is
45 degrees right so when you add 45 plus
45 you get 90 degree therefore that is
the solution for the part a let us look
at B which is 65 degrees now we know
that angle X plus angle y must be equal
to 90 degrees in order to satisfy the
complementary chytrid criterium so we
have 65 degrees plus angle Y giving us
90 degrees again transposing 65 degree
from the left-hand side to the right
hand side if you look at this this is
nothing but a simple algebraic equation
right it's a simple equation where the
value of y is unknown that's another way
of looking at it so we can we will say
that angle y equals
90 degrees minus sixty-five degrees
which when solved will give us so this
we are going to do 10-5 it gives me five
and this becomes 8 so 8 minus 6 is 2 so
we have 25 degrees right so 25 degrees
is the complement of angle which
measures 65 degrees now let us look at
sea and in see we have 41 degrees right
so let us use our criterion that is
angle X plus angle Y is 90 degrees
whereas angle X is 41 degrees plus angle
Y gives me 90 degrees now again we apply
the transpose that is we are transposing
this 41 degrees to the other side right
so we have only angle Y on the left-hand
side and we have 90 degrees minus 41
degrees now when we solve this we get 9
10 minus 1 is 9 and eight minus 4 is 4
so we get 49 degrees there for the
compliment of an angle with measures 41
degrees is 49 degrees let us look at
problem d now indeed we have the angle
that is given to us is 54 degrees so we
will again apply our criteria of angle x
plus angle Y the sum of these two angles
being equal to 90 degrees right or in
other words we will say that 54 degrees
plus angle y equals 90 degrees now we
will be transposing the angle Y to the
others sorry the 54 degrees to the other
side so we have angled y equals
90 degrees minus fifty-four degrees and
when I do the subtraction what I have as
10-4 gives me six and here it becomes
8-5 so it will be giving me 36 degrees
so angle Y is 36 degrees therefore 36
degrees is the complement of an angle
that measures 54 degrees so this is how
we can find out the complement of an
angle now let us look at another
interesting example which kind of
involves an algebraic equation and also
the concept of complementary angles so
the problem statement says the
difference in difference in measures of
two complementary angles is 12 degrees
find the measures of the angles now what
we know is that there are two angles
which are complementary and if we take
their difference right it comes out to
be 12 degrees so this is all what we
know and we have to find out both of
those angles so first let us draw a nice
partition here and so let us first start
with the information that we are given
the first thing that we know is the
difference right but before that we need
to assume the angles so I'll stick with
our earlier let angle X and angle Y be
the two angles
now let us say first try to form an
equation which kind of satisfies this so
we say it is it has been told that a
difference in measures of two
complementary angles is 12 so it simply
says that angle X minus angle why it
should give me 12 degrees this is what I
know let me just term it as the first
equation okay now is there anything else
that we can do to find out the values of
X&Y well we do know that the angles are
complementary and when we know the
angles are complementary we know that
there's some there is anger x plus angle
why that should be equal to 90 degrees
right so this is equation 2 so now we
have these two equations simple
equations and we have to find out the
value of x and y right so let's do one
thing we can try to represent angle X in
terms of angled while using the equation
1 so what we do is we will transpose the
Y to the right hand side so we have Y on
the left hand side will transpose it to
the other side so i can say that angle x
equals 12 degrees plus angle why now
this is our third equation right so we
got an angle x which is represented term
of angle Y now we can use this value of
angle X in equation 2 so that we get em
everything as angle wide right sorry so
let's substitute this 12 12 degrees
presented y into equation 2 so we have
12 degrees plus angle Y which is X right
this is watering subject 4x plus angle
y equals 90 degrees now we can simplify
this so we have 12 degrees plus twice of
angle Y that is equal to 90 degrees now
i can again transpose the 12 degrees on
the right hand side so we will have
twice of angle y equals 90 degrees minus
12 and when we carry out this
subtraction we have 10 minus two is
eight and eight minus 1 is 7 so we have
twice of angled y equal 78 degrees now
let us simplify this a bit further so
what we will do is we'll multiply both
the sides by half or in other words i'll
divide both the sides by two so we have
twice of angle Y divided by 2 equals 78
/ 2 so this 2 gets cancelled out and
here we have 2 times 3 is 6 and 2 times
9 is 18 so we get angle y equals 39
degrees right so this is how we found
out the first answer we found out the
value of angle Y now we can find out the
value of angle x using this equation or
we can even we can even use the equation
number 2 but let us use the first
equation here because in fact the third
equation right that we have this
equation here angle x equals 12 plus
angle Y is actually derived from the
first one so let us use this equation 3
to find out the value of angle X so
angle X is equal to 12 plus angle y
which is equal to 12 + 39
so when we carry out this edition we
have 9 plus 2 is 11 and 300 400 x we
have 51 degrees right so we can say that
the two angles are
39 degrees and 51 degrees and you can
even validate that these two values they
satisfy equation one and equation two so
if you do angle X which is 51 degree
minus 39 you will get 12 that is also
correct and if you add 50 1 + 39 that is
these two if you add you will get 90
degrees so it satisfies both the
equations therefore this is a solution
to the problem given here so that was
quite an interesting problem in the next
video we will learn about supplementary
angles