Two intersecting lines create four angles with the same vertex, labeled A

Question

, B
, C
, and D
. Angle B
is adjacent to ∠A
and ∠C
. Find m∠A
if m∠C=75°
.(1 point)
Responses

180°
180 degrees

75°
75 degrees

105°
105 degrees

15°

Answer 1

Since angles A, B, C, and D are formed by intersecting lines, we know that angles that are adjacent to each other are supplementary. This means that:

\[ m∠A + m∠B = 180° \] \[ m∠C + m∠D = 180° \]

Given that \( m∠C = 75° \), we can find \( m∠D \):

\[ m∠D = 180° - m∠C = 180° - 75° = 105° \]

Now since \( m∠A \) and \( m∠C \) are opposite angles (also called vertical angles), they are equal:

\[ m∠A = m∠C = 75° \]

Thus, the answer is:

75°.