Two intersecting lines create four angles with the same vertex, labeled A , B , C , and D . Angle B is adjacent to ∠A and ∠C . Find m∠A if m∠C=75° .(1 point)

Question

Responses

15°
15 degrees

75°
75 degrees

180°
180 degrees

105°

Answer 1

Since angle B is adjacent to angles A and C, and angle C is given as 75°, angle B must also be 75°.

Since angles A, B, C, and D form a complete rotation around the vertex, the sum of their measures must be 360°.

Therefore, to find angle A, we can subtract the measures of angles B and C from 360°:

360° - 75° - 75° = 210°

So, m∠A = 210°.

Answer 2

this is not one of the answers

Answer 3

I apologize for the confusion. In that case, let's approach the problem again.

Since angle C is given as 75°, and angle B is adjacent to angles A and C, angle B must also be 75°.

Since angles A, B, C, and D form a complete rotation around the vertex, the sum of their measures must be 360°.

To find angle A, we can subtract the measures of angles B and C from 360°:

360° - 75° - 75° = 210°

So, m∠A = 210°.

Answer 4

210 isnt one of the answers, whats the answer from the ones i sent

Answer 5

I apologize for the mistake. From the options provided, the correct answer is 105°.

Since angle B is adjacent to both angle A and angle C, and angle C is given as 75°, angle B must also be 75°.

The sum of the angles around a point must be 360°.

So, to find angle A, we subtract the measures of angles B and C from 360°:

360° - 75° - 75° = 210°

However, since angle A is adjacent to angle B, it must be supplementary to angle B. Therefore, angle A must be:

180° - 75° = 105°

So, m∠A = 105°.