construct 135 degree angle using compass
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hey yar here is ur answer
To construct 135 degree angle we first construct 90 degree angle and its steps of constructions are as follows:
1). Use ruler and draw a Line segment OB of any convenient length.
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 .
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 .
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
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 .
6). Join OE and extent it to A.
7). Above formed angle AOB = 90 Degree .
8) . Extend BO to Z .
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 .
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. ()
12). Join OF and extend to E .
13). EO is the bisector of Angle AOB.
Therefore, Angle AOE = Angle EOB = ½ of Angle AOB = 45 Degree each
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 ��� (Statement 2)
From Statement 1 and 2, we get:
Angle ZOE = 135�
To construct 135 degree angle we first construct 90 degree angle and its steps of constructions are as follows:
1). Use ruler and draw a Line segment OB of any convenient length.
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 .
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 .
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
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 .
6). Join OE and extent it to A.
7). Above formed angle AOB = 90 Degree .
8) . Extend BO to Z .
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 .
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. ()
12). Join OF and extend to E .
13). EO is the bisector of Angle AOB.
Therefore, Angle AOE = Angle EOB = ½ of Angle AOB = 45 Degree each
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 ��� (Statement 2)
From Statement 1 and 2, we get:
Angle ZOE = 135�
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