Question

Two angles that can be trisected with a straightedge and compass are _____ and _____ angles.

Answer 1

The answer is B. 90, 45 angle

Answer 2

Answer:

The correct option is B.

Step-by-step explanation:

Using the straightedge and compass we can construct the angles which are multiple of 15.

A angle can be trisected with a straightedge and compass if and only if one third of the angle is divisible by 15.

 $90 \div 3 = 30\text{ possible ( because 30 is multiple of 15 )}$

 $45 \div 3 = 15\text{ possible ( because 30 is multiple of 15 )}$

 $30 \div 3 = 10\text{ Not possible (because 10 is not multiple of 15)}$

 $75 \div 3 = 25\text{ Not possible (because 10 is not multiple of 15)}$

 $60 \div 3 = 20\text{ Not possible (because 10 is not multiple of 15)}$

It means 30, 75 and 60 can not be trisected with a straightedge and compass. So options A, C and D are incorrect.

Two angles that can be trisected with a straightedge and compass are 90° and 45° angles. The option B is correct.