Question

question 7 of 10 which pairs of angles in the figure below are vertical angles? check all that apply. a. ∠rtp and ∠atb b. ∠btd and ∠atp c. ∠dtn and ∠atp d. ∠atn and ∠rtd

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

\(\angle RTP\) and \(\angle ATB\) are not formed by the intersection of the same two lines, so they are not vertical angles.

Step3: Analyze Option B

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

Step4: Analyze Option C

\(\angle DTN\) and \(\angle ATP\) are not formed by the intersection of the same two lines, so they are not vertical angles.

Step5: Analyze Option D

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

Answer:

B. \(\angle BTD\) and \(\angle ATP\), D. \(\angle ATN\) and \(\angle RTD\)