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Let $x$ be the measure of the smaller angle and $y$ the measure of the greater angle. If the sum of these angles is $150_{∘},$ we can write the first equation. $x+y=150$ We also know that the measure of the smaller angle, $x,$ is $18_{∘}$ less than the measure of the greater angle, $y.$ This can be shown with an equation. $x=y−18$ Combining these equations we have the following system of equations. ${x+y=150x=y−18 $

b

To find the measure of the angles we need to solve the system ${x+y=150x=y−18 (I)(II) $ for $x$ and $y.$ When solving a system of equations using substitution, there are three steps.

- Isolate a variable in one of the equations.
- Substitute the expression for that variable into the other equation and solve.
- Substitute this solution into one of the equations and solve for the value of the other variable.

$x+y=150$

Substitute$x=y−18$

$y−18+y=150$

AddTermsAdd terms

$2y−18=150$

AddEqn$LHS+18=RHS+18$

$2y=168$

DivEqn$LHS/2=RHS/2$

$y=84$