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.
[tex]90 \div 3 = 30\text{ possible ( because 30 is multiple of 15 )}[/tex]
[tex]45 \div 3 = 15\text{ possible ( because 30 is multiple of 15 )}[/tex]
[tex]30 \div 3 = 10\text{ Not possible (because 10 is not multiple of 15)}[/tex]
[tex]75 \div 3 = 25\text{ Not possible (because 10 is not multiple of 15)}[/tex]
[tex]60 \div 3 = 20\text{ Not possible (because 10 is not multiple of 15)}[/tex]
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.
