Question

solving a situation by graphing a system of equations
the system of equations below represents the measures of 2 angles created by the diagonal of a rectangle:
x + y = 90
y = \frac{x}{5}
what is the measure of the greater angle?
what is the measure of the smaller angle?

Explanation:

Step1: Substitute $y$ into first - equation

Substitute $y = \frac{x}{5}$ into $x + y=90$, we get $x+\frac{x}{5}=90$.

Step2: Combine like - terms

Combine the $x$ terms: $\frac{5x + x}{5}=90$, which simplifies to $\frac{6x}{5}=90$.

Step3: Solve for $x$

Multiply both sides by $\frac{5}{6}$: $x = 90\times\frac{5}{6}=75$.

Step4: Solve for $y$

Substitute $x = 75$ into $y=\frac{x}{5}$, so $y=\frac{75}{5}=15$.

Answer:

The measure of the greater angle is $75^{\circ}$.
The measure of the smaller angle is $15^{\circ}$.