Question

name all of the angle(s) in the diagram that are adjacent and congruent to ∠bdc. choose the correct answer(s) below. select all that apply. a. ∠gdf b. ∠hdf c. ∠bdg d. ∠hde e. ∠gfd f. there are no angles adjacent and congruent to ∠bdc

Explanation:

Step1: Recall adjacent - angle definition

Adjacent angles share a common side and a common vertex.

Step2: Recall congruent - angle definition

Congruent angles have equal measures.

Step3: Analyze \(\angle BDC\)

• \(\angle BDG\) shares side \(BD\) with \(\angle BDC\) and the vertex \(D\). Also, vertical - angles are congruent. \(\angle BDC\) and \(\angle BDG\) are vertical - angles, so \(\angle BDC\cong\angle BDG\).
• \(\angle HDF\) and \(\angle BDC\) are vertical - angles. They are congruent and share the vertex \(D\). But they are not adjacent.
• \(\angle GFD\) has no relation of adjacency or congruence with \(\angle BDC\).
• \(\angle HDE\) has no relation of adjacency or congruence with \(\angle BDC\).
• \(\angle GDF\) has no relation of adjacency or congruence with \(\angle BDC\).

Answer:

C. \(\angle BDG\)