Question

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

A.90;30
B.90;45
C.60;45
D.75;90

Answer 1

The answer is B. 90, 45 angle

Answer 2

The correct option is B.

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 / 3 = 30\text{ possible ( because 30 is multiple of 15 )}`

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

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

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

`60 / 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.