Which of the following angles can be trisected using only a compass and straightedge? A.80° B.70° C.90° D.100°

The only angle from the options listed that can be trisected using only a compass and a straightedge is C. 90°.

The trisection of an angle is the division of the angle into three smaller angles, each of which has equal measure. It is well-known from classical geometry that some angles cannot be trisected using only the traditional tools of construction: a compass and a straightedge. This limitation falls under the category of "impossible constructions."

A 90° angle, also known as a right angle, can be trisected quite easily. You can bisect a 90° angle to get 45° and then bisect one of the 45° angles to get 22.5°. By doing this, you've effectively trisected the original 90° angle into three angles of 30°, 30°, and 30°, which can easily be achieved through a series of clear geometric constructions with a compass and straightedge.

For angles like 80°, 70°, and 100°, there is no general construction methodology that enables those angles to be trisected by the classical means, and indeed the act of trisecting an arbitrary angle has been proven mathematically impossible under the constraints of compass and straightedge constructions. This was proven as part of the famous three classical problems of antiquity, which perplexed mathematicians for centuries until they were proven to be insolvable or solved using more modern mathematical methods outside of the initial constraints.