Question

Using compass construct the angle $105°$

Answer 1

Step 1: Draw a line segment $\overline{AB}$ of any length

Step 2: Take compass and with A as centre measure any length as radius and draw a semi circle

Step 3: Lets take C as a point of intersection of circle and arc. With centre as C of same radius draw an arc on the semi circle

Step 4: Mark the new point as D ,With D as centre draw an another arc on the same circle

Step 5: Mark the new point as E

Step 6: With centre as D and E make an intersecting arc with same radius

Step 7: Mark the intersection of two arc as point F

Step 8: Join the point F and A using ruler and pencil

Step 9: Take a compass measure any distance on that, with E an G as centre draw a intersecting arc

Step 10: Mark the intersecting point as H

Step 11: Join the point A and H using ruler and pencil

Step 12: Now the angle $\angle CAH=105°$

Hence, the required angle $\angle CAH=105°$ is obtained.