Question

select the correct answer.
the sum of two complementary angles is 90°. 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.
a. ( \begin{cases} a + b = 90 \\ a - 2b = 15 end{cases} )
b. ( \begin{cases} a + b = 90 \\ 2b - 15 = a end{cases} )
c. ( \begin{cases} a + b = 90 \\ 2a - 15 = b end{cases} )
d. ( \begin{cases} a + b = 90 \\ 2b + 15 = a end{cases} )

Explanation:

Step1: Analyze complementary angles

Complementary angles sum to \(90^\circ\), so \(a + b=90\).

Step2: Analyze the relationship between \(a\) and \(b\)

The first angle \(a\) is 15 less than twice the second angle \(b\). Twice \(b\) is \(2b\), 15 less than that is \(2b - 15\), so \(a = 2b-15\) or \(2b - 15=a\).

Answer:

B. \( \boldsymbol{a + b = 90}\)
\( \boldsymbol{2b - 15 = a}\)