Question

what is the value of 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, $z + 47^{\circ}=(z - 50^{\circ})+z$.

Step2: Simplify the equation

Expand the right - hand side: $z + 47^{\circ}=z - 50^{\circ}+z$. Combine like terms: $z + 47^{\circ}=2z-50^{\circ}$.

Step3: Solve for z

Add $50^{\circ}$ to both sides: $z+47^{\circ}+50^{\circ}=2z$, which gives $z + 97^{\circ}=2z$. Subtract $z$ from both sides: $97^{\circ}=2z - z$.

Answer:

$z = 97^{\circ}$