Question

question 10 of 10 which pairs of angles in the figure below are vertical angles? check all that apply. a. ∠btd and ∠atp b. ∠rtp and ∠atb c. ∠atn and ∠rtd d. ∠dtn and ∠atp

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are formed when two lines intersect. They are opposite each other and are congruent.

Step2: Analyze Option A

\(\angle BTD\) and \(\angle ATP\) are formed by the intersection of lines \(AB\) and \(PD\). They are opposite each other, so they are vertical angles.

Step3: Analyze Option B

\(\angle RTP\) and \(\angle ATB\) are not formed by the intersection of the same two - line pairs. They are not vertical angles.

Step4: Analyze Option C

\(\angle ATN\) and \(\angle RTD\) are formed by the intersection of lines \(AN\) and \(RD\). They are opposite each other, so they are vertical angles.

Step5: Analyze Option D

\(\angle DTN\) and \(\angle ATP\) are not opposite each other with respect to a single intersection of two lines. They are not vertical angles.

Answer:

A. \(\angle BTD\) and \(\angle ATP\), C. \(\angle ATN\) and \(\angle RTD\)