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 theorem

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $7z + 15=(z + 44)+31$.

Step2: Simplify the right - hand side

$(z + 44)+31=z+75$. So the equation becomes $7z + 15=z + 75$.

Step3: Subtract z from both sides

$7z - z+15=z - z + 75$, which simplifies to $6z+15 = 75$.

Step4: Subtract 15 from both sides

$6z+15 - 15=75 - 15$, resulting in $6z=60$.

Step5: Solve for z

Divide both sides by 6: $\frac{6z}{6}=\frac{60}{6}$, so $z = 10$.

Answer:

$z = 10$