Solving a Problem Where the Difference of Two Complementary Angles is 20 Degrees
To find two complementary angles whose difference is degrees using a system of equations, assign variables and to their measures. Since the angles are complementary, their sum provides the first equation: . The given difference provides the second: . Using the elimination method, add the two equations together to cancel out , resulting in . Solving for gives . Finally, substitute into the first equation to find : , which yields . The measures of the two complementary angles are and .
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x + y = 90 x - y = 26
When using the elimination method, which characteristic of the variable 'y' should the welder recall as the primary reason that these two equations can be added together immediately to solve for x?
An HVAC technician is calculating two complementary angles, x and y, for a custom ductwork transition where the difference between the angles is 26 degrees. The technician sets up the following system of equations:
x + y = 90 x - y = 26
When the technician adds these two equations together to solve for x using the elimination method, which of the following is the correct resulting equation?
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