# which angle can't be constructed using ruler and 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  $\angle$ CAB  =  60$°$  And $\angle$ 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

$\angle$ 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

$\angle$ PAB  =  105$°$  .

Step 6 :  Now we take same radius and center C and Y , these arcs meet at Q . So we get

$\angle$ QAB  =  75$°$  .

Step 6 :  Now we take same radius and center C and X , these arcs meet at R . So we get

$\angle$ 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 20$°$ with help of compass , So we can't form angle of 5$°$ , 10$°$ , 20$°$ ,  40$°$ , 50$°$ ,  70$°$  , 80$°$ , ... with the help of compass .

• 5
maybe 10
• -3
those angles which do not come in the divisibility series of  360/2or3 cannot be made with the help of compass or ruler.
example-- 97, 77 etc.
• 6
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