Draw a horizontal line from the top left corner. Keep it selected.
With the Rotate tool click on the left end of your line and drag until Smart guides tell you that your line coincides with the slanting top edge of your trapezium. Smart Guides will say "path" or "anchor".
Now double click on the Rotate tool's icon and you will see the degree rotated in trhe dialogue box.
Press Cancel unless you want to rotate again.
1. SmartGudes on. (Because it's the only reliable snap feature.)
2. Line Tool: Draw a line from one end of the diagonal edge to the other.
4. DoubleClick the Line Tool. The dialog will tell you the angle & length of the path you just drew.
In both cases suggested by Steve and Jet, the Smart Guides label shows the angle while using the Rotate or Line tool, so double clicking these tools is not necessary unless you want to copy the value.
Also, with the Rotate tool you don't have to draw additional line. With nothing selected, click on one end of the line you want to measure to define the center of rotation, then click and drag from any place of the line towards the intersection with the center of rotation until the Smart Guides show the intersecting line. In this case the Smart Guides do not show the label but the Info panel will show the angle and double clicking the Rotate tool in the Tools panel will have it.
Here are two snapshots of measuring the angle with the Rotate tool when nothing is selected. The red arrows I painted over to show where the second click with the Rotate tool could be and the dragging direction
edit: Also you can check the measure tool and see if you like it. It is under the Eyedropper tool on the Tools panel. The problem is that it doesn't indicate snapping and I'm not sure if it actually does because dragging its end point appears to be snapping but without indication it could be coincidence.
double clicking these tools is not necessary unless you want to copy the value.
True, but if you want something less ephemeral than the Info panel or the Smart Guides readoff, the dialogue gives you something you can hold on screen while you are writing it down. I always have a tatty piece of paper to jot on while I'm working. Maybe not absolutely necessary but I have got used to working that way. Something to do with old dogs and new tricks :-)
I just check to see, and realized that the Info panel behaves in the same way as when checking by double clicking the Rotate tool. Even if you change tools and return to the Rotate tool the angle still stays until the Rotate tool is used again.
Me too :-)
Even though I'm using a digital pen and have one of its buttons programmed for double click, I still prefer keyboard shortcuts than mousing . Pressing R to get the tool if not already in use and pressing Enter gets the Rotate dialog. and Escape closes it which is not more difficult than Ctrl + F8 to get the Info panel.
i would to ask the following.i have made 2 examples.one is Jets and one technique is from collected suggestions and tutorials.
i am measuring the angle on which the line is angled upon and im getting 2 different results.
the 1st one is jets technique and the second one is the way im trying to find the angle.
but the result is not the same!although the angle is the same.
the 2nd way which i got the 45d is simple by making a line and using the rotate tool to give me the angle rotation of the magenta line.
315 = 360 - 45. Just two ways of saying the same thing, as measured anticlockwise and clockwise, presuming you start with a horizontal line and end with the slanting line. The former is the one used by the Rotation Tool and Object>Transform, unless you type -45.
And to repeat what was already said with an example, draw the line holding Shift dragging from left to right and the angle will show 0° then draw the same line in the opposite direction dragging from right to left and the angle will show 180°. Make the same test horizontlay and you get 90° and 270°.
Also have in mind that the Rotate tool repots the degrees differently than the Line tool, with plus and minus up to 180°. For example, the red arrow Tromboniator showed you on your image if drawn clockwise from the horizontal line down to the slanted line, the angle will show -45° and not 315°