Question

given the figure below, find the values of x and z.
(9x + 57)°
(5x + 69)°

Explanation:

Step1: Solve for \( x \)

Since \( (9x + 57)^{\circ} \) and \( (5x + 69)^{\circ} \) are vertical angles, they are equal.

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Step2: Solve for \( z \)

\( z^{\circ} \) and \( (9x + 57)^{\circ} \) are supplementary angles (they form a linear - pair). Substitute \( x = 3 \) into \( 9x+57 \):
\( 9x+57=9\times3 + 57=27+57 = 84 \)
Since \( z+(9x + 57)=180 \), then \( z=180-(9x + 57) \)
Substitute \( 9x + 57 = 84 \) into the equation:
\( z=180 - 84=96 \)

Answer:

\( x = 3 \), \( z = 96 \)