der Winkel
corner
A corner or a remote area in a room or place, often one that is hard to see into.
Die alte Truhe stand im hintersten Winkel des Dachbodens.
The old chest stood in the farthest corner of the attic.

corner / angle
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corner
A corner or a remote area in a room or place, often one that is hard to see into.
Die alte Truhe stand im hintersten Winkel des Dachbodens.
The old chest stood in the farthest corner of the attic.

You can tell from context whether a corner (meaning 1) or a geometric angle (meaning 2) is meant. Words like 'Raum' (room), 'Zimmer' (room), or 'dunkel' (dark) point to a corner, while 'Grad' (degrees), 'messen' (to measure), or 'spitz' (acute) refer to geometry.
Die Katze versteckte sich in einem dunklen Winkel hinter dem Sofa.
The cat hid in a dark corner behind the sofa.
The combination 'Ecken und Winkel' (nooks and crannies) is a fixed expression. It means that someone examines a place very thoroughly or refers to all parts of a place.
Er kennt alle Ecken und Winkel dieser Stadt.
He knows every nook and cranny of this city.
In a geometric context, 'Winkel' (angle) is often combined with certain adjectives to describe its size. The most important ones are 'rechter Winkel' (right angle, 90°), 'spitzer Winkel' (acute angle, <90°), and 'stumpfer Winkel' (obtuse angle, >90°).
Ein Quadrat hat vier rechte Winkel.
A square has four right angles.
The expression 'im toten Winkel' (in the blind spot) is a fixed term that is usually used in road traffic. It describes the area that a driver cannot see in the mirror.
Achte beim Radfahren immer auf den toten Winkel von Lastwagen.
When cycling, always watch out for trucks' blind spots.
degree
'der Grad' and 'der Winkel' both belong to geometry, so they are easy to confuse. 'der Winkel' is the space between two lines or surfaces that intersect. 'der Grad' is the unit of measurement used to state the size of this angle. So you can have an angle, and that angle has, for example, 90 degrees. The important point is: 'Winkel' is the geometric object, while 'Grad' is the number or unit used for measurement.

Im Matheunterricht zeichnet Lisa einen Winkel mit zwei Linien.
In math class, Lisa draws an angle with two lines.
Der rechte Winkel hat 90 Grad.
The right angle has 90 degrees.