Question

Three times the measure of the supplement of an angle is 108 degrees more than 9 times the measure of the angle's complement. Find the measure of the angle, it's complement and its supplement.

Answer 1

• 63°, 27°, 117°

Explanation:

• Angle = x
• Supplement = s
• Complement = c

Given

• 3s = 9c + 108°

We know that:

• s = 180° - x, as per definition of supplementary angles
• c = 90° - x, as per definition of complementary angles

Substituting in the equation above and solving for x:

• 3(180-x) = 9(90 -x) + 108
• 540 - 3x = 810 - 9x + 108
• 9x - 3x = 918 - 540
• 6x = 378
• x = 378/6
• x = 63°
• c = 90° - 63° = 27°
• s = 180° - 63° = 117°