Question

what is the value of z?

Explanation:

Step1: Identify angle sum property

Angles on a straight line sum to \(180^\circ\). The angles \(47^\circ\), \(z\), and the vertical angle to \(73^\circ\) (which is also \(73^\circ\)) form a straight line.

Step2: Set up the equation

\(47^\circ + z + 73^\circ = 180^\circ\)

Step3: Simplify and solve for \(z\)

First, add \(47^\circ\) and \(73^\circ\): \(47 + 73 = 120\). So the equation becomes \(z + 120^\circ = 180^\circ\). Subtract \(120^\circ\) from both sides: \(z = 180^\circ - 120^\circ = 60^\circ\).

Answer:

\(60^\circ\)