# 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$\xb0$ And $\angle $ DAB = 120$\xb0$

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$\xb0$ , 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$\xb0$ .

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

$\angle $ QAB = 75$\xb0$ .

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

$\angle $ RAB = 30$\xb0$ .

So we can construct so many angles with help of compass.

We only form angles 60$\xb0$ , 120$\xb0$ And angles between them As 90$\xb0$ , 45$\xb0$ , 150$\xb0$ or 30$\xb0$ , 15$\xb0$ , 75$\xb0$ or 22.5$\xb0$ . As we form these angle by dividing our angles in two equal parts . But as we can't form angle of 20$\xb0$ with help of compass , So we can't form angle of 5$\xb0$ , 10$\xb0$ , 20$\xb0$ , 40$\xb0$ , 50$\xb0$ , 70$\xb0$ , 80$\xb0$ , ... with the help of compass .

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