Question

question a: (14x - 23)° (7x - 7)°

Explanation:

Step1: Use the angle - sum property of adjacent angles

Since the sum of adjacent angles formed by a transversal intersecting two lines is \(180^{\circ}\), we have \((14x - 23)+(7x - 7)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(14x+7x-23 - 7=180\), which gives \(21x-30 = 180\).

Step3: Solve for \(x\)

Add \(30\) to both sides: \(21x=180 + 30\), so \(21x=210\). Then divide both sides by \(21\): \(x=\frac{210}{21}=10\).

Step4: Find the value of \(z\)

\(z\) and \((7x - 7)\) are vertical angles. Substitute \(x = 10\) into \((7x - 7)\): \(z=7\times10-7=70 - 7=63\).

Answer:

\(x = 10\), \(z=63\)