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Two lines AB and CD intersect each other at a point O such that ∠AOC: ∠AOD = 5:7. Find all the angles.

Answer:

Consider ∠AOC as 5x and ∠AOD as 7x

From the figure we know that ∠AOC and ∠AOD for linear pair of angles

So it can be written as

∠AOC + ∠AOD = 180

By substituting the values

5x + 7x = 180

On further calculation

12x = 180

By division

x = 180/12

x = 15

By substituting the value of x

∠AOC = 5x

So we get

∠AOC = 5 (15) = 75

∠AOD = 7x

So we get

∠AOD = 7 (15) = 105

From the figure we know that ∠AOC and ∠BOD are vertical angles

So we get

∠AOC = ∠BOD = 75

From the figure we know that ∠AOD and ∠BOC are vertical angles

So we get

∠AOD = ∠BOC = 105

"hello students welcome to leader
learning question answer video solutions
my name is biljot kaur and today's
mathematics problem is
two lines a b and c d intersects each
other at point o
such that aoc is to aod is 5 is to 7
now we have to figure out all the angles
now see guys
aoc is given as 5 since it's in the
ratio
so it's technically 5x similarly
this is 7x now
if you look at this thing this thing
forms a straight line
see guys this is a straight line that
means
we can use the identity of straight that
states that
x plus y
will give us 180 degree so
5x plus 7x will give
180 or you can say 12x
is equals to 180 or x is equals to
15. now since we have the value as x is
equals to 15
so if i put this value into
5x so i will get the value as 75
similarly if i put this value
in 7x so i will get 105.
so that means if i remove this
i can clearly say state that
[Music]
aoc is 75 degree
[Music]
and this is 105 degree
now since we know that vertically
opposite
angles are equal so angle a
o c is equals to angle b
o d and
angle c o b is equals to
a o d that means
this is also 75 degree and this is also
105 degree
because vertically opposite angles are
equal
vertically opposite angles
are equal thank you so much for watching
the video kids
if you have any questions any queries
please drop down in the comment section
for more fun videos subscribe to leo
have a wonderful day"

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