Question

given the figure below, find the values of \\(x\\) and \\(z\\).

\\(x = \square\\)
\\(z = \square\\)

Explanation:

Identify vertical angles

Find the relationship between opposite angles.
The angle \((9x + 46)^\circ\) and the angle \(73^\circ\) are vertical angles.
Therefore, they are equal:

$$(9x + 46) = 73$$

Solve for x

Using the Isolating Variables knowledge point:

$$
LATEXBLOCK0
$$

Identify supplementary angles

Find the relationship between adjacent angles on a straight line.
The angle \(z^\circ\) and the angle \(73^\circ\) form a linear pair.
Therefore, they are supplementary:

$$z + 73 = 180$$

Solve for z

Using the Isolating Variables knowledge point:

$$
LATEXBLOCK1
$$

Answer:

Given the figure below, find the values of \(x\) and \(z\).

\(x =\) <blank>3</blank>

\(z =\) <blank>107</blank>