Question

Which pairs of angles in the figure below are vertical angles? check all that apply

a. BTD and ATP
b. ATN and RTD
c.RTP and ATB
d. DTN and ATP​

Answer 1

The pairs of angles in the figure that are vertical angles are:

• a. BTD and ATP
• b. ATN and RTD

Step-by-step explanation:

To answer the question in the image, we need to understand what vertical angles are. Vertical angles are two angles that are opposite each other when two lines intersect. They are always equal in measure.

In the image, the following pairs of angles are vertical angles:

• Angle AOB and angle SOB
• Angle BOE and angle EOA
• Angle DOS and angle EOA
• Angle ATN and angle RTD
• Angle BTD and angle ATP

Therefore, the answer to the question is:

• A. BTD and ATP
• B. ATN and RTD

Rationale:

• Angle BTD and angle ATP are vertical angles because they are opposite each other when line BT intersects line AT.
• Angle ATN and angle RTD are vertical angles because they are opposite each other when line AT intersects line RD.

Calculation:

We can calculate the measure of each pair of vertical angles by using the following formula:

Vertical angle measure = 180 degrees - opposite angle measure

For example, to calculate the measure of angle BTD and angle ATP, we would use the following formula:

• Angle BTD measure = 180 degrees - angle ATP measure
• Angle ATP measure = 180 degrees - angle BTD measure

Since angle BTD and angle ATP are vertical angles, they have the same measure. Therefore, we can set the two equations equal to each other and solve for the measure of each angle:

Angle BTD measure = 180 degrees - angle BTD measure

2 * angle BTD measure = 180 degrees

angle BTD measure = 90 degrees

angle ATP measure = 90 degrees

We can use the same formula to calculate the measure of the other pairs of vertical angles in the image.

Conclusion:

The following pairs of angles in the image are vertical angles:

• Angle BTD and angle ATP (A)
• Angle ATN and angle RTD (B)