曲がる and 曲げる: street corners and bent knees
Compare changing direction in a street with bending an object or body part, separating a bent state from its cause.
Which corner to turn at
次の角を左に曲がってください。 directs someone to turn left at the next corner. With 曲がる, read まがる, 角を marks where the direction changes.
この道は川に沿って曲がっています。 says that the road curves along the river. It describes the shape of the road, not a person currently turning.
Bend a knee or wire
膝を少し曲げてください。 asks someone to bend their knees slightly. 曲げる, read まげる, marks the body part with を.
針金を丸く曲げました。 says that someone bent wire into a round shape. 丸く gives the resulting form, unlike 左に for a direction of travel.
Only the bent state is visible
傘の骨が曲がっています。 describes a bent umbrella rib. The sentence does not establish whether someone bent it by hand or strong wind caused it.
曲がる becomes 曲がって, while 曲げる becomes 曲げて. Although both 角を曲がる and 膝を曲げる contain を, one changes a route and the other bends a body part.
Is the corner an object physically bent in 次の角を左に曲がる?
Show the answer and why
No. The traveler turns left at the next corner. 角を marks that turning point.