Question

proving angles congruent
find the value of x
now, review the following steps. then, use the steps to solve a problem on your own.

1. using the definition of complementary angles, you know that the sum of the angle measures is equal to 90°.
2. combine like terms.
3. solve for x.

a. 18
b. 33
c. 9
d. 3
diagram: angles (4x - 3)° and (6x + 3)° with a right angle, indicating complementary angles

Explanation:

Step1: Identify complementary angles

The two angles \((4x - 3)^\circ\) and \((6x + 3)^\circ\) are complementary (sum to \(90^\circ\)) as they form a right angle. So, \((4x - 3)+(6x + 3)=90\).

Step2: Combine like terms

Simplify the left - hand side: \(4x - 3+6x + 3 = 10x\). The equation becomes \(10x=90\).

Step3: Solve for \(x\)

Divide both sides by 10: \(x=\frac{90}{10}=9\).

Answer:

\(x = 9\) (corresponding to option C)