Find the measure of an angle such that the difference between its supplement and 3 times its complement is 46°.

supplement means the sum of the two angles is 180° → y = 180 - x

complement means the sum of the two angles is 90° → y = 90 - x

supplement - 3(complement) = 46

(180 - x) - 3(90 - x) = 46

(180 - x) - 270 + 3x = 46

2x - 90 = 46

2x = 136

x = 68

68°

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.