The measure of angle θ is 7⁢𝜋4. The measure of its reference angle is °, and tan θ is .

The measure of angle θ is 7π/4. This is in radians. To convert it to degrees, we use the conversion factor 180/π.

Step 1: Convert 7π/4 to degrees 7π/4 * 180/π = 315 degrees

The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. For an angle of 315 degrees, the reference angle is 45 degrees because it's the smallest angle to the x-axis (either positive x-axis or negative x-axis).

Step 2: Determine the reference angle Reference angle = 360 - 315 = 45 degrees

The tangent of an angle in the fourth quadrant (like 315 degrees) is negative. The tangent of the reference angle (45 degrees) is 1, so the tangent of the original angle is -1.

Step 3: Determine the tangent of θ tan θ = -tan(45) = -1

So, the measure of its reference angle is 45 degrees, and tan θ is -1.