Examples: Angle Sum Property of a Triangle Video Lecture - Crash Course: Class 9

hello friends this video on lines and
angles part captain is brought to you by
exam viacom no more fear from exam so it
says that angle X is to really given
angle XY is that is 54 degree and if Z
and bisectors of these angles we have to
find Oh Z Y this angle Y over that this
angle so we can do it at you see these
two angles are given we can easily find
this angle this will be what 62 plus 54
and subtype by Devon this is 64 this
whole line will be 64 so this is angle
64 this angle small n will be how much
32 and this more I go so similarly this
is 54 this small angle how much 27 right
now you see we have to find this angle 1
this is earlier 32 degree and now seen
these two angles are they recognize
define this angle with this V X so X
plus 27 plus 32 is equal to 180 degree
so but this finding X is easy
yeah so I have formed X that is why it
was that I formed oh is that why that
why that is 32 degree and this is 123 we
just apply angles are property okay
sorry triangles of gravity so given that
a B is parallel to B E and B EC is 35
degree C D is 53 deviated by DC e
see this is something undefined and
given that these are parallel he'll
expand into him
see this is banner this is 30 by 8 this
is how much 35 so this is 30 by
alternate angle this is how much pretty
easy this will be what quality do you -
do you - anything that is 90 really you
can just write in the words right this
time here will be equal to this angle or
triangle buzz we know this angle in this
triangle we know these two angles
because my internet angle because some
of the angle in a triangle is 180 okay
line PQRS eq p qn RS they intersect each
other at pointy PRT is 45 what a degree
PRT r PT r PT 95 PS q is 75 we have to
find s QD s you have to find this pretty
easy see for finding this we need to
know this have you know that these two
angles are equal this angle is pretty
easy
how can you find 180 degree - these two
because some of these three is 180
degree this will be 180 minus ninety
five - forty
then you come on do it for debating this
angle is what I do this angle is 45
degree this angle opportunity
particulars like this is 45 this is 70
making even find this this px X plus 45
plus 75 if you add this you get 180 H of
X u s-- already you get 60 degree so
this is pretty easy and this PQ is
parallel perpendicular to PS this is PQ
p is 92 given PQ is parallel to SR PQ -
R upon s QR there's 28 degree s QR is 20
degree given QR t is 65 degree given we
have to find x + y so if you see these
two are parallel this hangar
by DT will be equal to X plus 23 correct
because PQ is parallel to SD alternate
angle so I can say that X plus 28 is
nothing but 65 degree so with this if
you solve exist nothing but 37 degree so
you found the value of x that this 37 so
once you the wanna find the value of x
we need to find the value of y plus in
this triangle sum is 180 degree this
angle is 90 already given this is 37
given so we can rewrite by y plus 90
degree plus 37 degree will be equal to
180 degree because in this triangle
pqs angle triangles angles are property
of a triangle you saw this you get the Y
value as 53 this is you can easily find
the value of x and y okay so let's take
one last question so it says that the
side Q R of triangle PQR is the triangle
PQR the side Q R this is produced to s
bisector of PQ r bisector of PRS they
mean at Point a so we have to prove that
QT r this angle you can do half of it
QPR this so let this be X and finally
prove that X okay and let's try to find
the value of this so these are bisector
like so to me this is a good one this
also be angle one and this is negative
do this about to be able to correct
because this is bisector qts bisector of
angle PQR so this booth angle our
vehicle PR bisector of angle p RL so we
essentially per okay so we know that
angle also we know that angle two will
be equal to 1 y plus y 2 plus angle
right here angle p RS nothing but angle
this angle is equal to this angle Plus
this angle exterior angle is going to do
some more opposite into your angle so PR
what - angle angle 2 is equal to and
then Y 2 plus twice angle this is one
relation we have one so angle Y is
nothing but twice off angle 2 minus
angle so we have got one traditional
Bengal boy okay same thing let's try to
find the value of angle X so you could
take this triangle take this right so in
this triangle angle t RS is equal to
angle qtr plus angle PQR okay because
this is external angle but internal
opposite angle so TRS is what able to
qtr is what angle X and this is what
angle one so angle X is 1 and 2 minus X
1 so comparing these two I can say that
what X is equal to Y by 2 because if you
see compare these two equations X is
going to twice off some values Y is
equal to sorry Y is going to twice of
some value and X is going to see mal
right into this angle 2 - angle 1
compare these two we can see that X that
is nothing but cm statement okay so
there's two a quick summary for a stance
on a line in the sum of the adjacent
angles so founders wanted a to be in
vice persons the line with three stands
for this this angle this angle
we'll always be 180 degree and the
reverse is also true into this called
linear axiom it was not true using
geometric instruction and observation we
have come up to the statement so it is
called linear pair axiom if two lines
intersect each other then the vertically
opposite angles are equal so angle 1 is
going to angle 2 in this case we are
called vertically opposite angle and
angle 3 is also equal to angle 4 in this
case they are also what degree of this
bangle if a transversal intersects two
parallel line then each pair of the
corresponding angles are equal each pair
of alternate interior angles are equal
and interview language is the same side
of the transversal supplement - that
means corresponding angles are equal if
you talk about all triangles this angle
this angle did you talk about angles of
the same side of the transversal
internal angle this angle sum is 1 unit
input transversal intersecting two lines
such that either any one pair of the
corresponding angle is equal any one
pair of the alternate angle interior
angle is equal or any one pair of
interior angles on the same side in the
supplementary then the lines are family
same thing whatever we told does the
converse this is the converse oh this
lines which are parallel to a given line
the parallel each other they have three
lines if L is parallel to M and let's
suppose M is parallel to M then L locks
we finally do and sum of three angles of
a triangle is mighty degree if you have
the angles in this us mo and all these
angles the son will always be 180 degree
if the size of the angle triangle is
produced the exterior angle so form is
equal to sum of two integers like this
angle one this is two
one will be equal to plus angle thank
you
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