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)
Responses

75°
75 degrees

105°
105 degrees

180°
180 degrees

15°
15 degrees

1 answer

To solve for \( m∠A \) when \( m∠C = 75° \), we use the properties of angles formed by two intersecting lines. The angles around the intersecting point sum up to \( 360° \), and for two adjacent angles, they are supplementary, meaning they add up to \( 180° \).

Since angles \( C \) and \( A \) are opposite angles, they are equal:

\[ m∠A = m∠C \]

Thus, if \( m∠C = 75° \), then:

\[ m∠A = 75° \]

Therefore, the correct response is:

75°