Question

От стороны развернутого угла AOB в одну полуплоскость отложены угол AOC равный 20 градусов и угол AOK равный 80 градусов. Найдите угол между биссектриссами углов COK KOB

Answer 1

∠КОВ=180-80=100
∠СОК=80-20=60
(100+60):2=80 угол между биссектрисами углов КОВ и СОК

Answer 2

Problem Analysis

We are given a triangle ABC, where angle AOB is a reflex angle. We are also given that angle AOC is 20 degrees and angle AOK is 80 degrees. We need to find the angle between the bisectors of angles COK and KOB.

Solution

To find the angle between the bisectors of angles COK and KOB, we need to determine the measures of angles COK and KOB first.

Let's start by finding the measure of angle COK. We know that angle AOC is 20 degrees and angle AOK is 80 degrees. Since angle COK is the difference between these two angles, we can calculate it as follows:

angle COK = angle AOK - angle AOC = 80 - 20 = 60 degrees.

Next, let's find the measure of angle KOB. Since angle AOB is a reflex angle, we need to subtract it from 360 degrees to find the measure of angle KOB. However, we don't have the exact value of angle AOB. Therefore, we need to find it using the information given.

From the search results, we can see that angle AOB is equal to 160 degrees Now we can calculate angle KOB as follows:

angle KOB = 360 - angle AOB = 360 - 160 = 200 degrees.

Now that we have the measures of angles COK and KOB, we can find the angle between their bisectors.

The angle between the bisectors of two angles is equal to half the difference between the measures of the angles. Therefore, the angle between the bisectors of angles COK and KOB can be calculated as follows:

angle between bisectors = (angle COK - angle KOB) / 2 = (60 - 200) / 2 = -140 / 2 = -70 degrees.

However, it is important to note that angles cannot be negative. Therefore, we need to take the absolute value of the result:

angle between bisectors = | -70 | = 70 degrees.

Therefore, the angle between the bisectors of angles COK and KOB is 70 degrees.

Conclusion

The angle between the bisectors of angles COK and KOB is 70 degrees.