Considering:
x = the missing angle
y = the complementary of angle x
z = the supplementary of angle x
To solve this question, follow the steps below.
Step 01: Write the equations that relate x with its complementary and supplementary angle.
Since complementary angles add up to 90:
x + y = 90°
Since supplementary angles add up to 180:
x + z = 180°
Step 02: Write an equation for the sum of the complement and supplement of x.
Given that: the sum of the measure of its complement and its supplement is 168°:
y + z = 168°
Step 03: Isolate y and z in the equation from step 01.
x + y = 90°
To isolate y, subtract x from both sides of the equation:
x + y - x = 90 -x
y = 90 - x
x + z = 180°
To isolate z, subtract x from both sides of the equation:
x + z - x = 180 -x
z = 180 - x
Step 04: Substitute the values of y and z found in step 3 in the equation from step 2.
y + z = 168°
90 - x + 180 - x = 168
Solving the equation by adding like-terms:
270 - 2x = 168
Subtracting 270 from both sides:
270 - 2x - 270 = 168 - 270
-2x = -102
Finally, dividing both sides by -2:
-2x/(-2) = -102/(-2)
x = 51°
Answer: The measure of the angle is 51°.