Knowing the angle COB 2 angle AOC, OD bisecting angle AOB, if the angle COD 20 degrees, find the deg

Answer: AOD is 6 degrees 40 minutes, or AOD is 60 degrees.

Solution process: Make a sketch of COD, and then add ray OA and OB: to the sketch according to the condition of OD bidivision AOB

From COb=2 AOC, it can be seen that ray OA is closer to ray OC than OB. That is, the rays OA and OC are on the same side of the straight line OD, and the ray OB is on the other side of the straight line OD.

The analysis shows that the radiation OA is either inside or outside the COD.

When ray OA is within COD, COB = 2 AOC, i.e., BOD + COD = 2 (COD - AOD).

i.e. aod + cod = 2 ( cod - aod).

Bringing in the known condition of cod = 20 degrees, we get aod = 20 3 degrees, i.e., 6 degrees and 40 minutes.

When ray OA is outside COD, COB=2 AOC

i.e. BOD + COD = 2 (AOD - COD).

i.e. aod + cod = 2 (aod - cod).

Bringing in the known condition of cod = 20 degrees, the solution is aod = 60 degrees.

Let AOC be X degrees, then COB is 2X degrees.

AOB is 3X degrees.

OD bisects AOB, then DOB is 3x 2 degrees.

cod=∠cob—∠dob

20＝2x—3x/2

Gives x = 40 degrees.

AOC is 40 degrees.

aod＝∠aoc＋∠cod

AOD 40 20 = 60 degrees.

AOD is 60 degrees.

Because the angle cob = the angle 2AOC

So angular AOC = angular AOB = 2 angular AOD

So the angle cod = angle aod + angle AOC = angle AOD + AOB angle = 3 angle AOD so angle AOD = angle cod 3 = 20 3 degrees.

Solution. aod

60 degrees, OC on the same side of the straight line OD, COB = 2 AOC, ray ob on the other side of the line OD Answer, COB = 2 AOC i.e. bod

COD2 (AODCOD i.e.

aodcod

2×（∠aod

COD carry-in.

COD 20 degrees.

known conditions. i.e. ray OA.

Analysis shows that it is either outside of COD.

When the ray OA is outside the COD, the ray OA is added to the sketch according to the condition of OD bisecting AOB, that is, 6 degrees 40 minutes

by cob=2 aoc, ob; 3 degrees, solution.

aod20, ie.

bodcod

2×（∠cod

AOD) i.e.

aodcod

2×（∠cod

AOD).

COD 20 degrees.

known conditions.

When the ray OA is within the COD, it can be seen that the ray OA is closer to the ray OC than the OB: the ray OA is either within the COD:

Make a sketch of the COD, or.

AOD is 60 degrees.

Answering process: AOD is 6 degrees 40 minutes.

Solution. aod

60 degrees, OC on the same side of the straight line OD, COB = 2 AOC, ray ob on the other side of the line OD Answer, COB = 2 AOC i.e. bod

COD2 (AODCOD i.e.

aodcod

2×（∠aod

COD carry-in.

COD 20 degrees.

known conditions. i.e. ray OA.

Analysis shows that it is either outside of COD.

When the ray OA is outside the COD, the ray OA is added to the sketch according to the condition of OD bisecting AOB, that is, 6 degrees 40 minutes

by cob=2 aoc, ob; 3 degrees, solution.

aod20, ie.

bodcod

2×（∠cod

AOD) i.e.

aodcod

2×（∠cod

AOD).

COD 20 degrees.

known conditions.

When the ray OA is within the COD, it can be seen that the ray OA is closer to the ray OC than the OB: the ray OA is either within the COD:

Make a sketch of the COD, or.

AOD is 60 degrees.

Answering process: AOD is 6 degrees 40 minutes.

Answer: AOD is 6 degrees 40 minutes, or AOD is 60 degrees to make a sketch of COD, and then add ray OA and OB to the sketch according to the condition of OD bisecting AOB: by COB=2 AOC, it can be seen that ray OA is closer to ray silver shirt OC. than OB

That is, the rays OA and OC are on the same side of the straight line OD, and the ray OB is on the other side of the straight sail line OD. The analysis can be known in the front car cavity: ...

Because the angle cob = 2 angle aoc, od bisects the angle mega aob, and the angle cod = 19 degrees, aob=3 aoc aod=1 2 aob=3 2 aoc= aoc+ cod so, cod=1 2 aoc=19 degrees, so, aob=19*2=38 degrees, so, aob=3 aoc=38*3=114 degrees.

If the angle AOC=x, then the angle COB=2X

OD bisects the angle AOB, then there is an angle collapse land attack AOD = angle BOD, that is: angle AOC + angle COD = angle BOD

x+19°=2x-19°

x = 38 ° of the group brother to the posture: angle aob = 2 angle aod = 2 * (38 ° + 19 °) = 114 °

Because od bisects the angle AOB

So the angle aod = angle dob = 1 2 angle aob

Because only the vertical angle AOD = angle AOC + angle COD

Angular cod = 14 degrees.

So the angle AOC + 14 = 1 angle AOB

Because the angle AOB = angle AOC + angle BOC

Angular BOC = 2 angular AOC

So angular AOC + 14 = 3 2 angular AOC

So the angle AOC = 28 degrees.

Because the angle AOD = angle AOC + angle COD

So Kadoyama Chang aod = 42 degrees.

So the angle dob = 42 degrees.

To sum up: the degree of angular AOC is 28 degrees, and the degree of angular DOB is 42 degrees.

Set the angle AOC = X then the angle COB = 2x the angle AOB = 3x the angle COB - the angle COD = the angle AOC + the angle COD

That is: 2x-20=x+20 solution x=40 so it's called aob=3x=120 I don't even bring the degree You add it yourself!

Solution: For the convenience of calculation, the degree of the angle AOB is set to X degrees.

OD bisects AOB (known).

aod= bod=x 2 (properties of isosceles triangles) cod=20 degrees (known).

cob=∠bod+∠cod=x/2+20,∠aoc=∠aod-∠cod=x/2-20

COB=2 AOC (known).

x/2+20=2(x/2-20)

Solve this equation to get x=120

Therefore, the degree of the angle AOB is 120 degrees.