Question

what is the value of z?
z = □°

Explanation:

Step1: Use the triangle angle sum theorem

The sum of angles in a triangle is \(180^{\circ}\). So, \((z - 4)+(z + 17)+61=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(z-4+z + 17+61=(z+z)+(-4 + 17+61)=2z+(13 + 61)=2z+74\).
The equation becomes \(2z+74 = 180\).

Step3: Solve for \(z\)

Subtract \(74\) from both sides: \(2z=180 - 74\), so \(2z=106\).
Divide both sides by \(2\): \(z=\frac{106}{2}\).

Answer:

\(z = 53\)