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 the property of same - side interior angles

Same - side interior angles are supplementary, that is, if two parallel lines are cut by a transversal, the sum of same - side interior angles is \(180^{\circ}\).

Step2: Calculate the measure of angle A

Let the given angle be \(125^{\circ}\). Since angle A and the \(125^{\circ}\) angle are same - side interior angles (assuming \(c\) and \(d\) are parallel and \(b\) is the transversal), we use the formula \(A + 125^{\circ}=180^{\circ}\). Then \(A = 180^{\circ}-125^{\circ}=55^{\circ}\). Alternate interior angles are equal, vertical angles are equal and corresponding angles are equal. But here the sum of the two angles (\(A\) and \(125^{\circ}\)) is \(180^{\circ}\) which is the property of same - side interior angles.

Answer:

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