I search and search but I am not able to find the simple solution.

How to draw a line perpendicular to another of any direction?

Thank you very much.

Welcome to the forum!

I don't think there is any simple way to do it.  But I'm sure we can help you find the easiest way.

As with many things in Inkscape, there are a few different ways to approach the problem.  And that might depend on the specific circumstances of your unique canvas. 

If I had just started drawing, and I need to draw a single object with a 90 degree angle, which does not start out horizontal or vertical, I would probably draw it horizontal or vertical and then rotate the finished object.  Or possibly I would use the Rectangle tool as a starting place to draw this object.

If I'm in the middle of a complex drawing, and I realize I need a 90 degree angle, I might use Guides.  Guides can be rotated (in the most recent versions of Inkscape anyway).  This would be my routine:

• drag out a guide and snap it to the first side of the angle
• rotate it around until it snaps to the other end of that line
• note the angle that guide turned out to be
• add or subtract 90
• create a new guide and rotate to that angle
• snap it to the first line, in such a way that I can make the 90 degree angle

Another way might be to use Object menu > Transform > Rotate.

• identify the angle of the first line
• calculate the needed angle for the 2nd line
• draw a horizontal or vertical line
• use Object menu > Transform > Rotate, to rotate it to the proper angle
• use node editing and the Node tool to connect it to the first line

Maybe other people will share other ideas?

Thank you very much. It's very kind of you. I hoped not to know an easy tool but it isn't. I used the Rectangle tool and the Transform menu but it is not really convenient. I didn't know the use of guides. Thank you.

Inkscape 1.0 has the 'draw perpendicular bisector' path effect, https://wiki.inkscape.org/wiki/index.php/Release_notes/1.0#Perpendicular_Bisector

Currently, Inkscape 1.0 is still in beta stage.

I came across this after I googled if there was a better way then my way (due OS stuff I am stuck on 0.92.2) and I wanted to share my solution.
My solution is probably to time consuming if you need to do a lot of angles, I just needed to do 2, so I was happy doing it this way.
I used geometry and math to fill in the positions of the third node. This way you get a second segment in a 90 degrees angle with the first and it will have the same length:

node 1:
x: 56.602 (x1)
y: 1596.361 (y1)

node 2:
x: 677.516 (x2)
y: 1514.976 (y2)

Then node 3 must be (to angle 'upwards'):
x: x2 + (y1 - y2) = 677.516 + (1596.361 - 1514.976) = 677.516 + 81.385 = 758.901 (x3)
y: y2 + (x2 - x1) = 1514.976 + (677.516 - 56.602) = 1514.976 + 620.914 = 2135.890 (y3)

There is a Snap Perpendicular option in the Document properties panel.

It's marvellous ! Thank you very much.