how to build an angle of 200 degree using compass and ruler
Answer :
We can construct angles , As we have shown in steps some of angle constructions .
Step 1 : Draw a line AB
Step 2 : Now take any radius in our compass . draw a semicircle , That meet at X our line AB .
Step 3 : Now we take center X and draw an arc with same radius that meet our semicircle at ' C ' And with same radius draw an arc taking center ' C ' that meet our semicircle at ' D ' .
Thats how we get CAB = 60 And DAB = 120
Step 4 : Now we draw two arcs as with same radius and center C and D , these arcs meet at E . So we get
EAB = 90 , Line AE meet our semicircle at 'Y'
Step 5 : Now we take same radius and center D and Y , these arcs meet at P . So we get
PAB = 105 .
Step 6 : Now we take same radius and center C and Y , these arcs meet at Q . So we get
QAB = 75 .
Step 6 : Now we take same radius and center C and X , these arcs meet at R . So we get
RAB = 30 .
So we can construct so many angles with help of compass.
We only form angles 60 , 120 And angles between them As 90 , 45 , 150 or 30 , 15 , 75 or 22.5 . As we form these angle by dividing our angles in two equal parts . But as we can't form angle of 200 with help of compass
We can construct angles , As we have shown in steps some of angle constructions .
Step 1 : Draw a line AB
Step 2 : Now take any radius in our compass . draw a semicircle , That meet at X our line AB .
Step 3 : Now we take center X and draw an arc with same radius that meet our semicircle at ' C ' And with same radius draw an arc taking center ' C ' that meet our semicircle at ' D ' .
Thats how we get CAB = 60 And DAB = 120
Step 4 : Now we draw two arcs as with same radius and center C and D , these arcs meet at E . So we get
EAB = 90 , Line AE meet our semicircle at 'Y'
Step 5 : Now we take same radius and center D and Y , these arcs meet at P . So we get
PAB = 105 .
Step 6 : Now we take same radius and center C and Y , these arcs meet at Q . So we get
QAB = 75 .
Step 6 : Now we take same radius and center C and X , these arcs meet at R . So we get
RAB = 30 .
So we can construct so many angles with help of compass.
We only form angles 60 , 120 And angles between them As 90 , 45 , 150 or 30 , 15 , 75 or 22.5 . As we form these angle by dividing our angles in two equal parts . But as we can't form angle of 200 with help of compass