Question

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

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, \(34z + 45=30 + 39z\).

Step2: Rearrange the equation

Subtract \(34z\) from both sides: \(45=30 + 39z-34z\).

Step3: Simplify the right - hand side

\(45 = 30+5z\).

Step4: Isolate the variable

Subtract 30 from both sides: \(45 - 30=5z\), which gives \(15 = 5z\).

Step5: Solve for \(z\)

Divide both sides by 5: \(z=\frac{15}{5}=3\).

Answer:

3