Question

What is the best answer here? help ASAP

Answer 1

Start with what can be true.

A is true no matter what else is. An angle whose endpoints (I and J in this case) are the endpoints of a diameter , make a right angle at K no matter where K. The only exception is that K cannot touch either I or J.

That fact does not make IK = KJ Move K closer to I and you will see that the two sides cannot be equal. C is incorrect.

By the same kind of reasoning B is wrong. The two acute angles need not be equal.

It the chords defining the arcs are not equal, neither are the arcs. D is not correct.

And because A is always true, E is false.

Answer 2

The angle subtended by a diameter is a right angle. That's Thales' Theorem (one of them anyway), sometimes thought to be the first theorem of geometry.

So the first choice is true.

The other angles are complementary, not necessarily congruent.

The sides and arcs aren't necessarily congruent either

Answer: first choice