# 45 Degree Angle

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### Detailed steps to construct an angle of 45 degrees:

In order to construct a 45 degree angle, first we will draw a 90 degree angle using the below mentioned steps:
1) Use a ruler to draw a line segment OB (of any length) 2) Now use a compass and open it to any convenient radius. With O as the center, draw an arc which cuts OB at X. 3) With X as the center and the radius as used in step 2, draw an arc which cuts the first arc at a point D. 4) With center as D and the radius as used in step 2, draw another arc which cuts the first arc at a point C. 5) With center as C and D and the radius as used in step 2, draw two arcs such that they cut each other at a point E. 6) Join points O and E and extent OE to a point A. 7) Angle AOB formed above is of 90 Degree.
Inorder, to construct an angle of 45 degree, we need to construct an angle bisector of angle AOB, using the steps written below.

8) Use compass, opened to any radius and with center as O, draw an arc which cuts OB at P and OA at Q. 9) With center as P and Q and the radius as used in step 8, draw two arcs such that they cut each other at a point F. 10) Join points O and F and extent OF to a point E. 11) EO is the bisector of Angle AOB i.e. Angle AOE = Angle EOB = 1/2 of Angle AOB = 45 Degree 