Question

a section of wall is being framed. a model of the framing work is shown below. which best describes the relationship between the 125° angle and angle a? they are same side interior angles. angle a measures 55°. they are alternate interior angles. angle a measures 125°. they are vertical angles. angle a measures 125°. they are corresponding angles. angle a measures 55°.

Explanation:

Step1: Recall same - side interior angles property

Same - side interior angles are two angles that are on the same side of the transversal and between the two parallel lines. The sum of same - side interior angles is \(180^{\circ}\).

Step2: Calculate angle \(A\)

Let the given angle be \(125^{\circ}\). If angle \(A\) and \(125^{\circ}\) are same - side interior angles, then \(A + 125^{\circ}=180^{\circ}\). Solving for \(A\), we get \(A = 180^{\circ}- 125^{\circ}=55^{\circ}\).

Step3: Analyze other angle relationships

• Alternate interior angles are equal. Since \(125^{\circ}

eq55^{\circ}\), they are not alternate interior angles.

• Vertical angles are equal. Since \(125^{\circ}

eq55^{\circ}\), they are not vertical angles.

• Corresponding angles are equal. Since \(125^{\circ}

eq55^{\circ}\), they are not corresponding angles.

Answer:

They are same side interior angles. Angle \(A\) measures \(55^{\circ}\).