Answer
You can enable Smart Guides U and use the Rotate tool R to measure an angle.
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With the Direct Selection tool A, select a line segment.
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Press R to engage the Rotate tool
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Click on the corner anchor to set it as the rotation centre
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Click and drag the line and rotate until it snaps to the other anchor. The Angle is displayed.
Finally, undo the changes using Ctrl+Z
Example
Attribution
Source : Link , Question Author : localhost , Answer Author : Billy Kerr