Final answer:
The statement '4 times the supplement of an angle exceeds 9 times the complement of the same angle by 55 degrees' is true when you set up and solve the corresponding equation, finding that the angle θ = 29° satisfies the condition.
Step-by-step explanation:
Answering a Trigonometry and Vectors QuestionThe statement '4 times the supplement of an angle exceeds 9 times the complement of the same angle by 55 degrees' is a mathematical condition that can be expressed using equations. In trigonometry and geometry, the supplement of an angle θ is always equal to 180° - θ, and the complement of the same angle is 90° - θ. By setting up the equation 4(180° - θ) = 9(90° - θ) + 55°, we check the validity of the statement.
Upon solving this equation, we find that 720° - 4θ = 810° - 9θ + 55°. Simplifying it leads to 5θ = 145°, so θ = 29°. Substituting back to check, 4(180° - 29°) = 604° and 9(90° - 29°) + 55° = 604°, confirming that the statement is indeed true.To solve this problem, we need to first understand what the supplement and complement of an angle mean. The supplement of an angle is the angle that, when added to the original angle, equals 180 degrees. The complement of an angle is the angle that, when added to the original angle, equals 90 degrees.Let's represent the angle as x. The supplement of the angle is 180 - x, and the complement of the angle is 90 - x.According to the given information, 4 times the supplement of the angle exceeds 9 times the complement of the angle by 55 degrees. We can write this as 4(180 - x) = 9(90 - x) + 55.Simplifying this equation, we get 720 - 4x = 810 - 9x + 55. Combine like terms and solve for x.