Question

find the values of x, y, and z in the triangle to the right.
$x = square$

Explanation:

Step1: Use the property of linear pairs

For the angle \(z\) and \((3x - 2)\), since they form a linear pair, \(z+(3x - 2)=180\), so \(z = 181-3x\). For the angle \(y\) and \((3x + 2)\), since they form a linear pair, \(y+(3x + 2)=180\), so \(y=179 - 3x\).

Step2: Use the triangle - angle sum property

In the triangle, \(x + y+z=180\). Substitute \(y = 179-3x\) and \(z = 181 - 3x\) into the equation:

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Answer:

\(x = 36\)