Question

1. consider the diagram. 9a solve for x.

Explanation:

Step1: Use the property of complementary angles

Since the two angles \((5x - 5)^{\circ}\) and \((2x+3)^{\circ}\) are complementary (their sum is \(90^{\circ}\)), we can write the equation \(5x - 5+2x + 3=90\).

Step2: Combine like terms

Combine the \(x\) - terms and the constant terms: \((5x+2x)+(-5 + 3)=90\), which simplifies to \(7x-2 = 90\).

Step3: Isolate the variable term

Add \(2\) to both sides of the equation: \(7x-2+2=90 + 2\), so \(7x=92\).

Step4: Solve for \(x\)

Divide both sides by \(7\): \(x=\frac{92}{7}\approx13.14\).

Answer:

\(x = \frac{92}{7}\)