Question

what is the value of z?
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Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(z + 49^{\circ}=(z - 47^{\circ})+z\).

Step2: Simplify the equation

Expand the right - hand side: \(z + 49^{\circ}=z - 47^{\circ}+z\).
Combine like terms: \(z + 49^{\circ}=2z-47^{\circ}\).

Step3: Solve for \(z\)

Subtract \(z\) from both sides: \(49^{\circ}=2z - z-47^{\circ}\).
Simplify: \(49^{\circ}=z - 47^{\circ}\).
Add \(47^{\circ}\) to both sides: \(z=49^{\circ}+47^{\circ}\).

Answer:

\(z = 96^{\circ}\)