Question

the sum of two complementary angles is \\(90^{\circ}\\). for one pair of complementary angles, the measure of the first angle is 15 less than twice the measure of the second angle. write a system of equations that can be used to determine the measure of the first angle, \\(a\\), and the measure of the second angle, \\(b\\).

\\(\

$$\begin{aligned} a + b &= 90 \\\\ 2a - 15 &= b \\end{aligned}$$

\\)

\\(\

$$\begin{aligned} a + b &= 90 \\\\ 2b - 15 &= a \\end{aligned}$$

\\)

\\(\

$$\begin{aligned} a + b &= 90 \\\\ a - 2b &= 15 \\end{aligned}$$

\\)

\\(\

$$\begin{aligned} a + b &= 90 \\\\ 2b + 15 &= a \\end{aligned}$$

\\)

Explanation:

Translate the complementary angles relationship

$$ a + b = 90 $$

Translate the second relationship

$$ a = 2b - 15 $$

Match with the given options

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Answer:

• (A) \(

$$\begin{aligned} a + b &= 90 \\ 2a - 15 &= b \end{aligned}$$

\)

• **(B) \(

$$\begin{aligned} a + b &= 90 \\ 2b - 15 &= a \end{aligned}$$

\) (Correct answer)**

• (C) \(

$$\begin{aligned} a + b &= 90 \\ a - 2b &= 15 \end{aligned}$$

\)

• (D) \(

$$\begin{aligned} a + b &= 90 \\ 2b + 15 &= a \end{aligned}$$

\)