1Cademy - Solving a Supplementary Angle Problem Using a System of Equations by Substitution

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Solving a Supplementary Angle Problem Using a System of Equations by Substitution

To find the measures of two supplementary angles where the larger angle is $12$ degrees less than five times the smaller angle, a system of linear equations can be solved using substitution. Let $x$ be the measure of the smaller angle and $y$ be the larger. Since supplementary angles sum to $180$ degrees, the first equation is $x + y = 180$ . The translation of the relationship stated in the problem provides the second equation: $y = 5x - 12$ . Substitute the expression for $y$ into the first equation to form $x + (5x - 12) = 180$ . Combining the $x$ terms yields $6x - 12 = 180$ . Adding $12$ to both sides results in $6x = 192$ , and dividing by $6$ gives $x = 32$ . Substituting $x = 32$ into the second equation produces $y = 5(32) - 12 = 160 - 12 = 148$ . This confirms the two angles measure $32^{\circ}$ and $148^{\circ}$ .

Updated 2026-04-24

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