Question

Mark all statements that are true.

A. An angle that measures 2π/3 is a reflex angle.
B. An angle that measure 170° is an obtuse angle.
C. An acute angle is one that measures less than π/2 but more than π/4.
D. An angle that measures 95° is an acute angle.

I know D. is NOT the answer and...

B. is ONE of the ANSWERS

I am just not sure about A. and C.

Please help and explain. Thank you!

Answer 1

If you look at the unit circle the angle for 2pi/3 is 120 degrees. Reflex angles are greater than 180 but less than 360.
Again if you look at the unit circle pi/2 is 90 degrees and pi/4 is 45 degrees.
Do these statements seem to ring true? :)

Answer 2

So I guess it would just be B.?

A FALSE 2π/3 is 120 degrees which is in the interval 90-180 it is obtuse
B TRUE 170 is in the interval 90-180
C FALSE An acute angle can be any angle between 0 and 90, not just between π/4 and π/2
D FALSE 95° is obtuse

Answer 3

Good job. :)