Question

construction the following angles using ruler and compass only. 30,45,60,75,90,120 and 135​

Answer 1

Steps to construct 30,45,60,75,90,120 and 135 angles. Step1:Draw a line AB and take a point O on it. Draw an arc with O as centre and any radius such that it cuts AB at two points C and D.

Step 2: With C as centre and same radius ,draw an arc intersecting the previous arc at E. 60 degree angle is formed.

Step 3:With E as centre and same radius, draw an arc intersecting the arc at F. 120 degree angle is formed.

Step 4: Taking E and F as centres , draw two arcs which intersect at each other at G. Join OG, which intersect the arc at H .90 degree angle is formed.

Step 5: Bisect 60 degrees to get 30 degrees.

Step 6: Bisect 90 degrees to get 45 degrees.

Step 7: Now taking H and D as centres draw two arcs intersect in I. Join OI.

Angle GOI=1/2 Angle GOA=45 Degrees

Angle IOB= Angle GOB+Angle GOI

=90 Degrees + 45 Degrees =135 degrees.

Step 8: Now taking H and E as centres, draw two arcs which intersect in I. Join OL.

Angle EOL=Angle GHI=1/2 Angle GOE=1/2 ×30 Degrees =15 Degrees

Angle IOB= Angle EOF+ Angle EOB

=15 Degrees +60 Degrees = 75 degrees

All the angles are formed. Please like this answer