Question

find the value of each variable.
y =
z =

Explanation:

Step1: Find z

Angles on a straight line sum to \(180^\circ\). So, \(z + 113^\circ = 180^\circ\). Solving for \(z\), we get \(z = 180 - 113 = 67^\circ\).

Step2: Find y

The sum of interior angles of a quadrilateral is \(360^\circ\). So, \(y + 100^\circ + 83^\circ + z = 360^\circ\). We know \(z = 67^\circ\), substitute: \(y + 100 + 83 + 67 = 360\). Simplify: \(y + 250 = 360\). Solve for \(y\): \(y = 360 - 250 = 110^\circ\).

Answer:

\(y = 110\), \(z = 67\)