Question

given the figure below, find the values of x and z.
(9x + 38)°
(5x + 86)°
z°
x =
z =

Explanation:

Step1: Identify Vertical Angles

The angles \( (9x + 38)^\circ \) and \( (5x + 86)^\circ \) are vertical angles, so they are equal.

$$ 9x + 38 = 5x + 86 $$

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:

$$ 4x + 38 = 86 $$

Subtract 38 from both sides:

$$ 4x = 48 $$

Divide by 4:

$$ x = 12 $$

Step3: Find the Measure of the Angle

Substitute \( x = 12 \) into \( 9x + 38 \):

$$ 9(12) + 38 = 108 + 38 = 146^\circ $$

Step4: Find \( z \)

The angle \( z^\circ \) and the angle \( 146^\circ \) are supplementary (they form a linear pair), so their sum is \( 180^\circ \).

$$ z + 146 = 180 $$

Subtract 146 from both sides:

$$ z = 34 $$

Answer:

\( x = 12 \)
\( z = 34 \)