Question

find the value of each variable.
(there is a quadrilateral with angles 102°, 89°, y°, and z°, and an adjacent angle of 106° to z°.)
y =
z =

Explanation:

Step1: Find z using supplementary angles

Supplementary angles sum to \(180^\circ\). So \(z + 106^\circ = 180^\circ\), which gives \(z = 180 - 106 = 74^\circ\).

Step2: Find y using quadrilateral angle sum

The sum of interior angles of a quadrilateral is \(360^\circ\). Let the angles be \(z = 74^\circ\), \(102^\circ\), \(89^\circ\), and \(y\). So \(74 + 102 + 89 + y = 360\). Calculating the sum of known angles: \(74 + 102 + 89 = 265\). Then \(y = 360 - 265 = 95^\circ\).

Answer:

\(y = 95\), \(z = 74\)