Question

what is the value of z?

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

$$
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$$

Step3: Solve for \(z\)

Subtract \(z\) from both sides: \(49=2z - 47 - z\), which simplifies to \(49=z - 47\). Then add \(47\) to both sides: \(z=49 + 47\).

Answer:

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