Question

making angle of 135 degree with compass and ruler​

Answer 1

Answer:

1). Use ruler and draw a Line segment OB of any convenient length. (as shown below)

2). Now use compass and open it to any convenient radius. And with O as center , draw an arc which cuts line segment OB at X . (as shown below)

3). Again use compass and opened to the same radius (as of step 2). And with X as center , draw an arc which cuts first arc at D . (as shown below)

4). Again use compass and opened to the same radius (as of step 2). And with D as center , draw another arc which cuts first arc at C . (as shown below)

5). Again use compass and opened to the same radius (as of step 2). And With C & D as center, draw two arc which cuts each other at E . (as shown below)

6). Join OE and extent it to A. (as shown below)

7). Above formed angle AOB = 90 Degree .

8) . Extend BO to Z . (as shown below)

9). Since ZB is a straight line, so formed Angle AOZ = 90 Degree (angle sum property)

Now, to construct at 135 degree angle, we will construct the angle bisector of above angle AOB. And its done in the following steps:

10). Again use compass and open it to any convenient radius. And with O as center , draw an arc which cuts line segment OB at P and OA at Q . (as shown below)

11). Again use compass and opened to same radius (as of step 10).And with P & Q as center and, draw two arcs which cuts each other at point F. (as shown below)

12). Join OF and extend to E . (as shown below)

13). EO is the bisector of Angle AOB.

Therefore, Angle AOE = Angle EOB = ½ of Angle AOB = 45 Degree each (as shown below)

14). Now observe that:

Angle ZOA = 90°

Angle AOE = 45°

Add both the angles and we get

Angle ZOA + Angle AOE = 90° + 45° ..... (Statement 1)

Now observe the above diagram:

Angle ZOA + Angle AOE = Angle ZOE .....nhi (Statement 2)

From Statement 1 and 2, we get:

Angle ZOE = 135° (as highlighted with pink color)

Answer 2

Answer:

first draw a 60 degree angle n then a 120 degree

..

..

then put your compass on the 120 degree mark and bisect the angle between 120 and 180

later on u will get 140 degree ....again bisect the angle between 120 n 140

.....u ll get 130

now bisect between 130 n 140

u will 135 degree.

That's it

hope it helps