Two angles are complementary. The measure of the larger angle is 55? less than twice the measure of the smaller angle. If x measures the smaller angle and y measures the larger angle, write a system of two equations in two unknowns that would model the situation.
A) $\left\{ \begin{array} { l }
x + y = 90 \
y = 2 x - 55
\end{array} \right.$
B) $\left\{ \begin{array} { l }
x + y = 90 \
y = 55 - 2 x
\end{array} \right.$
C) $\left\{ \begin{array} { l }
x + y = 180 \
y = 2 x - 55
\end{array} \right.$
D) $\left\{ \begin{array} { l }
x + y = 180 \
y = 55 - 2 x
\end{array} \right.$

Question

Two angles are complementary. The measure of the larger angle is 55? less than twice the measure of the smaller angle. If x measures the smaller angle and y measures the larger angle, write a system of two equations in two unknowns that would model the situation.
A) $\left\{ \begin{array} { l } 
x + y = 90 \
y = 2 x - 55
\end{array} \right.$
B) $\left\{ \begin{array} { l } 
x + y = 90 \
y = 55 - 2 x
\end{array} \right.$
C) $\left\{ \begin{array} { l } 
x + y = 180 \
y = 2 x - 55
\end{array} \right.$
D) $\left\{ \begin{array} { l } 
x + y = 180 \
y = 55 - 2 x
\end{array} \right.$

Quizplus · Accepted Answer

We know that two angles are complementary, so their sum is 90 degrees. We can represent the larger angle as y and the smaller angle as x.

From the problem statement, we are also given that:

- The larger angle is 55 degrees less than twice the measure of the smaller angle. This can be written as y = 2x - 55.

Putting these two equations together gives us the system:

\begin{cases} x + y = 90 \ y = 2x - 55 \end{cases}

Therefore, the answer is (A).

Two Angles Are Complementary {x+y=90y=2x−55\left\{ \begin{array} { l } x + y = 90 \\y = 2 x - 55\end{array} \right.{x+y=90y=2x−55​

Two Angles Are Complementary $\left\{ \begin{array} { l } x + y = 90 \\y = 2 x - 55\end{array} \right.$