Question

in the figure below, \\(j \parallel h\\).
find the values of \\(z\\) and \\(x\\).
\\(z = 18\\)
\\(x = 75\\)

Explanation:

⚡ Using what you learned: lines and angles (parallel, transversal, vertical)

Step 1: Find the value of \( z \)

Since lines \( j \) and \( h \) are parallel (\( j \parallel h \)), the interior angles on the same side of the transversal are consecutive interior angles, which are supplementary:

$$ 75 + z = 180 $$

$$ z = 105 $$

Step 2: Find the value of \( x \)

The angle labeled \( z^\circ \) and the angle labeled \( (3x + 21)^\circ \) are vertical angles, which means they are equal:

$$ 3x + 21 = z $$

Substitute \( z = 105 \):

$$ 3x + 21 = 105 $$

$$ 3x = 84 $$

$$ x = 28 $$

Answer:

$$ z = 105 $$

$$ x = 28 $$