In the Extended version of Photoshop, select Analysis > Set Measurement Scale> Custom to customize the Measurement scale To display this scale in the Info panel use the flyout to select Panel Options and check the Measurement Scale option.
The Ruler tool can be used to measure an angle like a protractor. Drag the first line and then Option (Mac) / Alt (Win) -click on the either endpoint and drag out the second line. The angle can be viewed in either the Options bar or the Info panel.
Taking a measurement with the Ruler tool and then selecting Image > Image Rotation> Arbitrary will automatically enter the measurement in the Rotate Canvas dialog box.