Question

How to construct 80 degree?

Answer 1

As 80 is motnot a multiple of 15, it becomes a little complex to draw it with compass , but since you asked for it .

Only by using compass , 80° angle to be constructed…

As 90° - 10° = 80° , So, we try to construct 10° first

We need to know that any angle can be divided into any number of 2^n equal parts. Where n is a whole number like 1, 2, 3,4 ….. & so on.

Step wise , shown below are angles to be constructed in order..

Step1: 90° + 45° = 135°

Step2: 135° ÷ 2 = 67.5°

Step3: 67.5° ÷2 = 33.75°

Step4: 33.75° ÷2 = 16.875°

Step4: Now, we combine angles 33.75° & 16.875° together to get 50.625°

Step4: Now, from our initial 90° angle , the above constructed 50.625 ° is taken off. & We are left with 40° approximately or we can say very very close to 40°. ( as with 100% accuracy, it's not possible to construct the required measure only by using compass)

Step4: Now this 40° is divided into 2 equal parts. We get 20°, which is further divided into 2 equal parts . We get 10°

Step5: Now we construct a fresh 90° angle, out of which the above obtained 10° is cut off. ( by using the method of construction of equal angles)

Finally we get 90° - 10° = 80°

In the above method, we are neglecting the lowest decimal value… Whereas in other methods, we may have to neglect the bigger decimal value, which affects the accuracy more.