Examples: Properties of Parallelogram(Part 2) Video Lecture | Advance Learner Course: Mathematics (Maths) Class 7

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quadrilaterals part 16 is brought to you
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exam question number 5 the measures of
two adjacent angles of a parallelogram
are in the ratio three is to to find the
measure of each angle of the
parallelogram so let us assume that the
angles are so let's assume that the
angles be 3x and 2x so let us assume
that these would be the angles now as
for the property of parallelogram we
know that sum of adjacent angles in a
parallelogram is equal to 180 degrees
so therefore 3x plus 2x should be equal
to 180 degree or we can say 5 X will be
equal to 180 degrees or X would be equal
to 180 degrees divided by 5 so this
would be 36 so X would be equal to 36
degree therefore the angles would be
equal to 3 into 36 degree which would be
equal to 108 degree and the other angle
would be 2 into 36 degree that is 72
degrees therefore the angles would be 72
degrees and 108 degrees
question number 6 the adjacent figure
Hope is a parallelogram as you see here
this is a parallelogram find XY and Z
okay so here again we will make use of
the properties of parallelogram so first
of all I think we will try to find out
this angle it is called this angle 1 now
if you see here angle 1 plus 70 degree
will be equal to 180 degree right
because this is the straight angle
therefore angle 1 will be equal to 180
degree minus 70 degree which would be
nothing but 110 degree now as for the
property of parallel
program we know that opposite angles in
a parallelogram are equal therefore we
can say that X will be equal to angle 1
which is equal to 110 degree therefore
the value of x would be hundred 10
degree now let us talk about the other
angles let us talk about the triangle e
HP now from triangle HPV no eggs we know
for T we do not know this angle so if we
are able to find out this angle we
should be able to find out Z because Z
is equal to this angle right so let us
call this angle as angle 2 so in
triangle e HP the sum of the three
angles that is X plus 40 degree plus
angle tool will be equal to 180 degrees
now since EP is parallel to o H
therefore angle 2 will be equal to angle
Z so we can write it as X plus 40 degree
plus Z is equal to 180 degree or X is
hundred ten degree plus 40 degree plus Z
is equal to 180 degrees
or we can say Zed is equal to 180 minus
150 which is equal to 30 degree so
that's how we found out the value of Z
so now what we are left with we are left
with the value of y so now we know said
we know angle one so all we are left out
with is angle Y but do we really need to
do so much of calculation to find out
angle Y it's not needed because we know
this angle is 40 degree and angle Y is
equal to 40 degree right because these
are again alternate angles since e H is
parallel to open therefore these are
alternate angles so this is how we could
find x y&z question number 7 find x and
y so here we see a parallelogram are UN
s and also its diagonals which meet at a
let's call this pointless oh and we know
by property that diagonals of a
parallelogram
they bisect each other so we will make
use of this property to solve this
question now since we know that
diagonals bisect each other that means
our Oh will be equal to o n that is 16
will be equal to X plus 1 this is one
equation that we get also S 4 will be
equal to o u or this can be written as
20 will be equal to y plus 7 so let us
call this equation 2 now we will solve
the equation 2 to get the value of y
which is 20 minus 7 that is equal to 30
now we put the value of y is equal to 13
in equation 1 so what do we get 16 is
equal to X plus 13 or we can say x is
equal to 16 minus 13 which is equal to 3
so this is how we can calculate the
value of x and y question number 8 in
the figure both risk and clue are
parallelograms so our I SK this is one
parallelogram and this is another
parallelogram they have been drawn in
such a way that they intersect each
other for certain regions some part of
it is common for both the parallelograms
so we have to find out the value of x so
here we gain here you make use of this
property that opposite angles of a
parallelogram are equal now when you
look at this parallelogram clue so when
you look at the parallelogram you you
would see that angle e is equal to 70
degree so angle e is equal to 70 degree
because these are opposite angles now
let us focus on the other parallelogram
this risk so in this parallelogram if
you see angle K plus angle s will be
equal to 180 degree because angle K and
angle s these two are adjacent angles at
the sum of the adjacent angles is equal
to 180 degree so from this angle s will
be equal to 180 degree minus angle K
that is 180 degree minus 120 degree
which is equal to 60 degree so now if
you look at let us call this point as
point O so now if you look at triangle
Oh II s what do you see
you know angle e you angle you know
angle s so all that you need to find is
s X so we know that sum of three angles
of a triangle is equal to 180 degrees so
here let's put the value of angle S
which is 60 degree angle E which is 70
degree and this is equal to 180 degree
therefore X is equal to 180 degree minus
130 degree which is equal to 50 degree
therefore the value of x would be 50
degrees question number nine find the
measure of angle B and angle s if SP is
parallel to our Q so SP and ad Q and
parallel so let's see what would be the
measure of angle B and angle s now just
before we go ahead with a problem can
you tell me if this is a fan melodrama
the PQRS which you see on the screen
this is not a parallelogram because not
both pairs of opposite sides are
parallel only one pair of opposite side
a parallel RS is not parallel to P Q
therefore this is not a parallelogram so
can you tell me which type of
quadrilateral is this this is nothing
but a trapezium because one of the pair
of sides are parallel so this is a
trapezium she'll here what do we see we
see that this angle is given as 130 this
angle is given as 90 and it is mentioned
that s P is parallel to our Q now when
these two are
so if this is 90 so this would also be
90 so if this is also 90 this entire
thing is 180 so this also has to be 90
so therefore angle s will also be equal
to 90 degree now we know that the sum of
the four angles interior angles in a
quadrilateral is equal to 360 degrees so
we can say angle B plus angle Q plus
angle R plus angle s all the interior
angles they sum to their sum would be
360 degree so P is not known Q is 130
rs90
s is also 90 so this is equal to 360
so therefore this comes out to be angle
P plus 310 degrees is equal to 360
degrees or angle P is equal to 360
degree - 310 degree which is equal to 50
degrees so therefore we could find angle
B as 50 and angle s as 90 degrees
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