1Cademy - Solving a Complementary Angle Problem Using a System of Equations by Elimination

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Solving a Complementary Angle Problem Using a System of Equations by Elimination

To solve the system of equations for finding two complementary angles where their difference is $26$ degrees, apply the method of elimination. First, establish variables where $x$ represents the measure of the first angle and $y$ represents the second. The geometric relationship demands that complementary angles sum to $90$ degrees, yielding the first equation: $x + y = 90$ . The problem statement gives a second equation: $x - y = 26$ . Adding these two equations directly eliminates $y$ because its coefficients are already opposites, giving $2x = 116$ . Dividing by $2$ results in $x = 58$ . Next, substitute $x = 58$ back into the first sum equation to get $58 + y = 90$ , which simplifies to $y = 32$ . Verifying the results, $58 + 32 = 90$ and $58 - 32 = 26$ . Therefore, the two angles measure $58^{\circ}$ and $32^{\circ}$ .

Updated 2026-04-24

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