Question

the image shows a portion of a staircase railing. there are three parallel rails supported by two posts. the transversal shown is parallel to the posts. what is true about the angles formed by the intersection of railings and the post? choose one option from each drop - down menu to answer the question. ∠bcd has the same measure as choose.... if ∠gfj measures x°, then the measure of ∠hik is choose.... the sum of the measures of ∠cfe and choose... is 180°.

Explanation:

Step1: Identify corresponding angles

Since the transversal is parallel to the posts and the three posts are parallel, by the property of parallel lines and transversals, \(\angle BCD\) and \(\angle FEC\) are corresponding angles. So \(\angle BCD\) has the same measure as \(\angle FEC\).

Step2: Use linear - pair property

\(\angle CFE\) and \(\angle GFE\) form a linear pair. Given \(\angle GFE=x^{\circ}\), and \(\angle CFE + \angle GFE=180^{\circ}\) (linear - pair of angles). Also, since the transversal is parallel to the posts and the posts are parallel, \(\angle HIK\) and \(\angle GFE\) are corresponding angles. So if \(\angle GFE = x^{\circ}\), then \(\angle HIK=x^{\circ}\)

Answer:

\(\angle BCD\) has the same measure as \(\angle FEC\); if \(\angle GFE\) measures \(x^{\circ}\), then the measure of \(\angle HIK\) is \(x^{\circ}\); the sum of the measures of \(\angle CFE\) and \(\angle GFE\) is \(180^{\circ}\)