270,023 views
1 vote
1 vote
find the measure of an angle such that the sun of the measure of its complement and its supplement is 168 degrees

User David Rosson
by
2.9k points

1 Answer

24 votes
24 votes

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°.

User Pengibot
by
3.0k points