# The measure of a supplement of an angle is 6 times the measure of the complement of the angle. Find the measure of the angle, its supplement, and its complementInclude sources, explanation, and work.

taylormath | High School Teacher | (Level 2) Adjunct Educator

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Two angles are complimentary if they sum to 90 degrees.  Two angles are supplementary if their sum is 180 degrees. To find the solution, 3 variables exist.

x: The measure of the angle

y: The measure of the supplement

z: The measure of the complement

Equations:

x+y=180 (sum of supplemental angles is 180 degrees)

x+z=90 (sum of complementary angles is 90 degrees)

y=6z (The supplementary angle is 6 times the complementary angle)

Using substitution for y, the top equation becomes x+6z=180.

Using elimination with x+6z=180 and subtracting x+z=90, the result is 5z=90 and z=18.  So the complementary angle is 18 degrees.

x=90-18=72

y=6(18)=108 or y=180-72

The solution checks when the measure of the angle is 72, the measure of the supplement is 108, and the measure of the compliment is 18.

qwertymak | Student, Grade 10 | (Level 1) Honors

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Let us assume that the given angle is x

Supplement of x = 180-x

Complement of x = 90 - x

Given supplement of x = 6*complement of x

=> 180-x=6(90-x)

=> 180-x=540-6x

=> 6x-x=540-180

=> 5x= 360

=> x = 72

Therefore

Supplement of 72 = 108

Complement of 72 = 18