Question

solve for the missing angles in the two diagrams below. solve for t.

Explanation:

Step1: Identify angle - pair relationship in first diagram

The two lines are parallel. The given angle of 83° and angle \(z\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal.
So, \(z = 83^{\circ}\)

Step2: Analyze second - set of parallel lines

In the second diagram, \(AB\parallel CD\) and \(FE\) is a transversal. We are not asked to solve for angles in this part, so we skip it.

Step3: Identify angle - pair relationship in third diagram

The given angle and angle \(t\) are supplementary (they form a linear - pair). The sum of angles in a linear - pair is 180°. Let the given angle be 100°. Then \(t=180 - 100\)
\(t = 80^{\circ}\)

Answer:

\(z = 83^{\circ},t = 80^{\circ}\)