Examples: Polygons and Angle Sum Property of Quadrilaterals Video Lecture | Advance Learner Course: Mathematics (Maths) Class 7

hello friends this video on
quadrilaterals part 9 is brought to you
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so based on all the basics that we have
learned so far on polygon or diagonals
or quadrilaterals and their properties
let us try to solve some of the
questions question number one how many
diagonals does each of the following
half a convex quadrilateral so any
convex quadrilateral how would it look
like maybe something like this a convex
quadrilateral quadrilateral enemies will
have four sides and since it is a convex
quadrilateral it would be a bulging
quadrilateral where all the internal
angles are less than 180 degrees now
here how many diagonals can be drawn
this is one diagonal and this is another
diagonals so maximum we can draw two
diagonals now when you talk about a
regular X 7 or a cube the hexagon is one
with six sides and regular means the
sides are equal and the angles are also
equal so values of the length of all
these sides are equal and also the
internal angles are equal so in this
case how many diagonals can be drawn so
we can actually draw any diagonals let's
see in fact let's name this let us call
this as a b c d e f now from point a let
us try to join all the non consecutive
vertices because they are the diagonals
so from a we could draw three diagonals
from B let us try to draw the diagonals
we could draw a one two and three so
from B also we could draw three
diagonals from C now C is already
connected to a C is not connected to F
so let's draw this now C is also not
connected to e so from C we could draw
how many diagonals we could draw three
diagonals so basically let's try writing
also so for a we could draw three
diagonals
being again we could draw three
diagonals for C we could draw two
diagonals what about D so you see D is
already connected to B D is also
connected to a but D is not connected to
F so from D to F we can draw only one
diagonals so for D we can draw one
diagonal for E from E to C already
connected E to be already connected to a
already connected so from easy to not
need to draw in further diagonal so that
means these are the total number of
diagonals that we can have in regular
hexagons
so this comes out to be nine when you
look at the triangle a triangle has
three sides so let's name this a B and C
so here we will actually have zero
diagonals you know why because when you
diagonal is that line segment with joins
two non-consecutive vertices but here
you don't have any non-consecutive
vertices so for a both B and C are
consecutive but X similarly for B both a
and C are consecutive vertices for C
again a and B are consecutive vertices
so we really do not have any non
consecutive vertices to be connected by
a diagonal therefore the number of
diagonals in a triangle is zero question
number two what is a regular polygon
States the name of a regular polygon of
three sides four sides and six sides so
as mentioned before so in a regular
polygon all the sides and all the angles
would be equal and obviously it has to
be a polygon that is it has to be a
simple closed curve made up of only line
segments now what would we call a
polygon with three sides so a polygon
with three sides would be a triangle 3
means trial polygon with four sides
would be a quadrilateral and a polygon
with six sides would be a hex 7 do you
think I missed out something the
question of
asked the name of a regular polygon now
these would be just polygons so
quadrilateral is a polygon with four
sides but it is not a regular polygon
because all the quadrilaterals they do
not have they're all sides and all
angles equal so that means which is that
type of quadrilateral which has all
sides and all angles equal yes
absolutely that is a square so square
would be a regular polygon with four
sides similarly which is that triangle
which has all sides and all angles equal
yes absolutely that is equilateral
triangle and when we talk about hexagon
what would be that X again that would be
nothing but a regular hexagon so the
moment we say regular hexagon that would
mean that all the sides of the hexagon
are equal and therefore all their angles
are also equal question number three
find X now here what is this falling in
which type of polygon it has four sides
one two three four so this is a
quadrilateral and what do we know this X
is one of the internal interior angles
of the quadrilateral now we know that
the in sum of the interior angles is
equal to how much sum of interior angles
of a quadrilateral is equal to 360
degrees now basically the formula is n
minus two into 180 degrees but here n
would be four so therefore we would get
sum of the interior angles 360 degree so
here what are the interior angles 50
plus 130 plus 120 plus X is equal to 360
degrees therefore we can say this entire
value would be 300 degrees plus X is
equal to 360 degrees therefore X will be
equal to 360 degrees minus 300 degrees
which would be nothing but 60 degrees
therefore the value of X is 3 6 is 60
degrees
question number 4 again find X so here
if you
this is again a quadrilateral therefore
the angle sum of interior angle a and
the interior angles sum here also would
be equal to 360 degree so we have 70
degree plus 60 degree plus how much
would be this angle so if this is 90
degrees this is also 90 degree because
the sum of these two angles is a
straight line which is 180 degree so
this would be 90 degrees plus X is equal
to 360 degrees so this entire value is
220 degree plus X is equal to 360 degree
or we can say X is equal to 360 degree
minus 220 degree which is equal to 140
degrees so that's the value of X thank
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