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

180°
180 degrees

105°
105 degrees

15°
15 degrees

75°

Answer 1

Since the lines intersect, the angles have the following relationships:

• Angles A and C are opposite angles (vertical angles), which means they are equal: \( m∠A = m∠C \).
• Angles A and B are adjacent angles that are supplementary, meaning their measures add up to 180°: \( m∠A + m∠B = 180° \).

Given that \( m∠C = 75° \), we can use the relationship with angle A: \[ m∠A = m∠C = 75° \]

Thus, the measure of angle A is: \[ m∠A = 75° \]

The answer is 75°.