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геометрия

7класс

эльмирарафикова

угол

решениезадачи

задачи

мектеп

школа

mektep

mekteп

mekteponline

мектепонлайн

мектепонлайнгеометрия

00:00:04

Hello guys, here I am again, I'm Olga

00:00:07

Rinatovna

00:00:08

and in a geometry lesson we are

00:00:12

solving problems on the topic of angle. In previous

00:00:18

lessons we looked at the concept of an

00:00:20

angle and now we are solving practical

00:00:23

tasks. The task sounds like this: the ray

00:00:28

of the eye and o m passes between the sides of the angle

00:00:34

a and b you need to find the angle to m if the angle a

00:00:41

y b is equal to 90 degrees and oka is equal to 40

00:00:45

degrees and m and b is equal to 30 degrees,

00:00:48

first we write down the conditions of the problem we are

00:00:53

given given two rays while

00:00:55

and o.m. so I write down given a

00:01:03

ray that divides angle a and b or

00:01:12

that passes between the sides of angle a

00:01:14

and b know I must write down that we are

00:01:17

given a geometric figure angle we

00:01:21

need to find the angle a and b if angle a and b are

00:01:29

equal 90 degrees angle a oka is equal to 40

00:01:36

degrees and angle m and b is equal to 30 degrees

00:01:43

find find

00:01:48

corner o and of course angle a at b we

00:01:53

need to put degrees in order for the guys to

00:01:57

solve this problem, I always advise

00:02:00

first of all to build a drawing drawing

00:02:05

where we would you can clearly see what kind of

00:02:09

figure this is, how the rays divide this angle,

00:02:12

and in general, what needs to be done, so we are

00:02:15

building the corner of the lip, angle a and b, why remove it, we

00:02:20

start from the corner a y because we are

00:02:22

told that the rays oka and o m divide the angle a

00:02:29

y or passes between the sides of angle a,

00:02:32

designate angle b is equal to 90 degrees, we

00:02:36

need to construct, in principle, here it’s

00:02:39

great, we have angle a at b is equal to 90

00:02:41

degrees and I built it,

00:02:44

angle a at b is equal to 90 degrees, I want to

00:02:48

remind you that if the angle is equal to 90

00:02:52

degrees, then this right angle and I

00:02:57

built 90 degrees, then

00:03:00

the rays are drawn inside soooo k is equal to 40

00:03:05

degrees some rays

00:03:07

I immediately want to note that in the figure in the

00:03:13

geometry section, of course it is advisable

00:03:16

to adhere to these values, but this is not a

00:03:21

gross mistake if you do not build an

00:03:23

oak angle equal to 40 degrees of course you

00:03:27

need to think about the fact that forty degrees

00:03:29

is naturally an acute angle, that it

00:03:31

should be built

00:03:34

somewhere around 40 degrees inside this angle, but

00:03:39

this is not a critical mistake if

00:03:43

you can’t build this angle of exactly 40 degrees

00:03:46

because we studied the construction of angles

00:03:48

in in the fifth grade, further the angle m and b is

00:03:52

equal to 30 degrees, that is, we have drawn a ray

00:03:55

of the eye, we will immediately indicate that it is equal to 40

00:03:58

degrees further than m and b is equal to 30 degrees,

00:04:03

this confuses you a little, that is, there

00:04:05

must be some kind of ray, some are not

00:04:07

confused by some ray o m and then the angle

00:04:13

will be m and b is equal to 30 degrees, but

00:04:19

if you find it difficult, then you can

00:04:24

read the angle the other way around.

00:04:26

that is, these are from here most often

00:04:30

when several rays are drawn inside the corner,

00:04:35

you begin to get confused

00:04:37

where these rays are located, so first

00:04:40

build as it was written down for you, but if you

00:04:43

find it difficult,

00:04:44

go on the other side, that is, I went from the

00:04:46

corner and then you will succeed, and

00:04:48

now we need to find the angle to m after

00:04:51

we have constructed

00:04:53

this drawing, this drawing probably

00:04:56

we can clearly see everything perfectly what needs to be

00:04:58

done, you already know, and so if the angle ooo

00:05:01

were equal to 90 degrees, this entire

00:05:05

angle is equal to 90 degrees and this angle is

00:05:09

40 and this is 30, then you can find the angle koru and

00:05:13

but we need to write it down correctly and

00:05:15

so, according to the axiom,

00:05:18

the size of the angle we have is always equal to the sum of the

00:05:22

parts or the sum of the angles into which

00:05:27

its rays are divided, that is, the angle a about b for

00:05:33

us is equal to the sum of angles

00:05:35

a oka oka plus corner

00:05:42

o because this is the first corner this is 2

00:05:46

this is 3 which interests us at the moment

00:05:48

of course there are more angles here but for now they

00:05:50

interest us further plus the angle k o m k

00:05:54

o m and plus the guys angle m a b m o b and

00:06:02

now instead of angle a y b I sign 90

00:06:09

degrees 90 degrees instead of angle ouka I

00:06:16

sign 40 degrees k o m we need to

00:06:21

find the unknown I so I write it k

00:06:24

plus m a b we have equal 30 degrees and it’s

00:06:29

immediately clear what to find angle to m I

00:06:35

must

00:06:36

subtract 40 degrees from 90 degrees

00:06:39

and subtract 30 degrees here

00:06:43

the entry is possible 90 minus in parentheses 40

00:06:46

plus 30 and from here we have equal 90

00:06:53

minus 70 is 20 degrees we needed to

00:06:57

find the angle to m therefore in the answer I

00:07:01

write down the angle, it is equal to 20 degrees and

00:07:06

this is the correct solution and return the entry

00:07:09

only when we wrote down in a

00:07:12

literal expression

00:07:15

that an angle is always equal to the sum of its parts,

00:07:20

we can write

00:07:22

an axiom here, that is, we don’t just

00:07:26

write it like that, but we write it according to some

00:07:29

statements and

00:07:30

problem 2 these problems are often

00:07:35

encountered and cause slight

00:07:37

difficulties, let's still analyze

00:07:39

this problem and so the problem sounds like this: the ray of

00:07:42

the father

00:07:43

divides the angle a a b into two angles

00:07:49

you need to find cb

00:07:53

if the angle a b is equal to 78 degrees, the angle a and

00:07:59

c is less angles b and c by 18 degrees

00:08:07

father's beam divides the angle and ben has two angles guys

00:08:11

solving problems and designing problems you

00:08:14

can start by writing this

00:08:17

if you find it difficult, you can first

00:08:20

construct a drawing and then write it down and

00:08:23

so we know for sure that angle a a be

00:08:26

is broken by the beam fathers, let's

00:08:29

depict it and so the angle a a b is somewhere

00:08:37

like this

00:08:59

angle a and b into two parts and

00:09:05

one part is stipulated to be 18

00:09:09

degrees less than the other, well, it is clear that it is

00:09:12

divided so that one corner inside

00:09:15

will be larger, one corner will be smaller, well, let's

00:09:17

break it down somewhere like this c and then,

00:09:24

according to the condition, we will allow an angle angle option

00:09:30

we have more than an angle angle c b

00:09:36

that is, we can see 18 degrees here

00:09:41

and we need to find the leg fits we

00:09:49

need to find the angle x c c question and angle c and

00:09:56

b question this type of problem constantly

00:10:01

leads you to some kind of horror this or that, well, it

00:10:04

brings you some kind of discomfort,

00:10:06

why because if it were

00:10:09

said that the internal angle, well, let’s say

00:10:13

131 by 18,

00:10:16

then everything was great, but you

00:10:19

know this big angle, yes a a

00:10:22

b this big angle is known to you

00:10:26

us is equal to 78 degrees 78 degrees but

00:10:31

these guys have a large angle consisting of angle

00:10:34

a and c&c both are truly alive, that is, I have to

00:10:38

write down that angle a a be

00:10:42

to find it we need angle a father to

00:10:45

add angle clb but but

00:10:50

you don’t know either angle a c is not an angle c, both are

00:10:55

the only thing you know is that angle a is

00:10:58

greater than angle c and b by 18 degrees, what

00:11:04

needs to be done in this case, you need to clearly

00:11:06

know one algorithm,

00:11:08

that is, we don’t know this angle, we don’t

00:11:11

know this angle, not this angle we

00:11:15

don’t know then designate one of these

00:11:19

angles and cashiers and best of all I

00:11:22

advise you to designate the smallest one who is

00:11:25

smaller in size here it is clearly visible that c

00:11:28

and b are written like this and the fathers are greater than

00:11:31

co2 by 18 or I read

00:11:33

c and b less and here prices by 18, and

00:11:38

if I guys denote by x

00:11:42

and the angle option is 18 more

00:11:47

if this x and this one is 18 more as we

00:11:51

write on means plus more by

00:11:56

more plus then it will be x plus 18 and

00:12:00

now guys let's go back to our

00:12:05

expression for our record

00:12:07

and this record corresponds to the axiom

00:12:10

instead of and I would substitute the data here

00:12:15

it will be 78 degrees equal to now guys

00:12:19

why is everything written

00:12:21

in a column by a mathematician, it is desirable in order

00:12:24

not to miss anything not to miss nor

00:12:27

to deceive here is the angle out Sam and how

00:12:30

the option was designated we wrote it here and x

00:12:33

plus 18 x plus 18 Dutch further plus the

00:12:39

angle c removed us is equal to x that's all

00:12:43

I got I got

00:12:45

an equation so I have to solve this equation

00:12:47

78 degrees here I wrote -18

00:12:53

degrees equals x plus x will be 2x 78

00:12:57

-18 this will be 60 is equal to 2 x

00:13:02

from here x is equal to 30 degrees, that is, x is

00:13:06

equal to 30, you can directly write it down when you

00:13:10

return to this

00:13:12

it will be 30 degrees where to write it down,

00:13:15

let's write it here, we designated it as

00:13:17

30 degrees here, so here

00:13:21

we will have x plus 18 48 48 plus 30 be 78

00:13:28

is suitable and you can safely write down the answer

00:13:31

the answer we write down the answer angle option 48

00:13:40

degrees you can, in principle, directly

00:13:43

write it down to write x plus

00:13:46

18 substitute it or you can solve it orally and the

00:13:49

angle cdb is equal to 30 degrees this is

00:13:54

how the guys solve the problem of

00:13:56

finding the size of the angle on the following

00:13:58

in the lessons we will get acquainted with new

00:14:00

concepts and for today our lesson is finished,

00:14:03

goodbye until we meet again

00:14:05

[music]

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