Answer:
The reference angle for an angle whose measure is -440° is 80°.
Explanation:
The cycles for angles range from the traditional 0° to 360° and subsequent 360° ranges befor and after this traditional intervals, also have the same properties.
So, the ranges that exist and correspond to the traditional 0° to 360° include
0° to 360°
360° to 720°
720° to 1080°
And in the negative direction, we have
-360° to 0°
-720° to -360°
We can see that -440 is in the range of
-720° to -360°
Using the traditional 0° to 360° to compare this range of -720° to -360°, let x represent the reference angle in the traditional range that we require.
-720° ------ 0°
-440° ------ x
-360° ------ 360°
Using interpolation,
[-440° - (-720°)]/[-360° - (-440°)] = (x - 0°)/(360° - x)
(280/80) = x/(360-x)
3.5 = x/(360-x)
3.5(360 - x) = x
1260° - 3.5x = x
4.5x = 1260°
x = (1260°/4.5) = 280°
But, the reference angle is the smallest angle that one can make from the terminal side of an angle (that is, where the angle ends) with the x-axis. It uses the x-axis as its frame of reference.
So, 280° is a fourth quadrant angle, whose equivalent in the first quadrant is 360° - 280° = 80°
Hope this Helps!!!