Question

what is the value of z? write your answer as an integer or as a decimal rounded to the nearest tenth. z = °

Explanation:

Step1: Apply exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(10z + 47=12z+30\).

Step2: Rearrange the equation

Subtract \(10z\) from both sides: \(47 = 12z-10z + 30\), which simplifies to \(47=2z + 30\).

Step3: Solve for \(z\)

Subtract 30 from both sides: \(47 - 30=2z\), so \(17 = 2z\). Then divide both sides by 2: \(z=\frac{17}{2}=8.5\).

Answer:

\(z = 8.5\)