Question

what is the value of z? write your answer as an integer or as a decimal rounded to the nearest tenth. z = ___° (triangle with angles 32°, 7z - 17°, 2z - 2°)

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(32 + (7z - 17) + (2z - 2) = 180\).

Step2: Simplify the left side

Combine like terms: \(32 - 17 - 2 + 7z + 2z = 180\) → \(13 + 9z = 180\).

Step3: Solve for z

Subtract 13: \(9z = 180 - 13 = 167\). Divide by 9: \(z=\frac{167}{9}\approx18.6\).

Answer:

\(18.6\)