Question

example 1 complementary and supplementary angles
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the difference between the measures of two supplementary angles is 18°. the measure of the smaller angle is _, and the measure of the larger angle is _.

Explanation:

Step1: Let the measure of the smaller angle be $x$ and the larger angle be $y$.

We know that supplementary angles add up to $180^{\circ}$, so $x + y=180^{\circ}$. Also, $y - x = 18^{\circ}$.

Step2: Solve the system of equations.

Add the two equations together: $(x + y)+(y - x)=180^{\circ}+ 18^{\circ}$. This simplifies to $2y=198^{\circ}$, so $y = 99^{\circ}$.

Step3: Find the value of $x$.

Substitute $y = 99^{\circ}$ into $x + y=180^{\circ}$, we get $x=180^{\circ}-99^{\circ}=81^{\circ}$.

Answer:

The measure of the smaller angle is $81^{\circ}$, and the measure of the larger angle is $99^{\circ}$