Question

geometry sem a geometry
lines parallel
two lines, a and b, are crossed by a transversal.
complete an equation that justifies why lines a and b must be parallel, using
the converse of the same - side interior angles theorem.
enter your answers in the boxes.

Explanation:

Step1: Recall the converse of same - side interior angles theorem

The converse of the same - side interior angles theorem states that if two lines are cut by a transversal and the sum of the same - side interior angles is \(180^{\circ}\), then the two lines are parallel.

Step2: Identify the same - side interior angles

In the given figure, the two angles that are same - side interior angles are \(55^{\circ}\) and \(125^{\circ}\).

Step3: Write the equation

We need to check if their sum is \(180^{\circ}\). So the equation is \(55 + 125=180\).

Answer:

\(55+125 = 180\)