Question

Which angle measure is equivalent to the angle

17π/4 ?

A)230 ∘
B) 135∘
C) 45 ∘
D) 315 ∘

Answer 1

To convert the angle 17π/4 radians to degrees, we multiply by 180/π and subtract the full circles (multiples of 360 degrees) to find the equivalent angle within one rotation, which is 45 degrees.

Step-by-step explanation:

The question asks which angle measure is equivalent to the angle 17π/4. To find the equivalent angle in degrees, we need to convert the given radian measure to degrees using the conversion factor where π radians equals 180 degrees.

First, multiply 17 by 180 and divide by 4:

(17 × 180) / 4 = 765 degrees.

Since 765 degrees is greater than a full circle (360 degrees), we subtract the largest multiple of 360 degrees that is less than 765 to find the equivalent angle within one rotation:

765 - 360 × 2 = 765 - 720 = 45 degrees.

Therefore, the equivalent angle measure to 17π/4 radians is 45 degrees, which corresponds to option C.