Draw The Angle Of 135 Degree

To construct an angle of 45

1. Construct an angle of 90 .

Bisect it.

Construction of angle measuring 90

Steps of construction:

Step 1: Draw a ray OB.

Step 2: With O as the centre and any convenient radius, draw an arc MN, cutting ray OB at M.

Step 3: With M as the centre and the same radius, draw another arc, cutting arc MN at P.

Step 4: With P as the centre and the same radius draw, one more arc, cutting arc MN at Q.

Step 5: With P as the centre and radius more than (1/2)PQ and less than PQ, draw an arc above PQ.

Step 6: With Q as the centre and the same radius, draw another arc, cutting the previous arc at A.

Step 7: Draw a ray OA.

Angle AOB is the required angle of measure 90.

Bisection of Angle AOB

Step 8: Mark the point of intersection of arc MN and ray OA as X.

Step 9: With X as the centre and radius more than (1/2)XM and less than XM, draw an arc.

Step 10: With M as the centre and the same radius, draw another arc, intersecting the previous arc.

Step 11: Mark the point of intersection of the arcs as C.

Step 12: Draw a ray OC.

Angle COB is the required angle of measure 45.

Construction of angle measuring 135 :

To construct an angle of 135 :

Construct an angle of 90.

Construct an angle of 45 adjacent to it.

Construction of angle measuring 90 :

Steps of construction:

Step 1: Draw a line AB and mark a point O on it.

Step 2: With O as the centre and any convenient radius, draw an arc MN, cutting line AB at M and N.

Step 3: With M as the centre and the same radius, draw another arc, cutting arc MN at P.

Step 4: With P as the centre and the same radius, draw one more arc, cutting arc MN at Q.

Step 5: With P as the centre and radius more than (1/2)PQ and less than PQ, draw an arc above PQ.

Step 6: With Q as the centre and the same radius, draw another arc, cutting the previous arc at C.

Step 7: Draw ray OC. Angle COB is the required angle of measure 90.

Bisection of Angle AOC

Step 8: Mark the point of intersection of arc MN and ray OC as L.

Step 9: With L as the centre and radius more than (1/2)LN and less than LN, draw an arc.

Step 10: With N as the centre and the same radius, draw another arc,intersecting the previous arc at D.

Step 11: Draw ray OD.

m(BOD) = m(BOC) + m(COD)

= 90 + 45

= 135

Angle BOD is of measure 135.