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

180°
180 degrees

15°
15 degrees

105°

1 answer

Since angles B and C are adjacent to angle A and since the sum of the angles around a point is 360°, we can use the fact that angle A and angle C are complementary (they share a vertex and are adjacent).

Given that \( m∠C = 75° \), we can use the relationship between angles adjacent to each other since they form a straight line together with angle A:

\[ m∠A + m∠C = 180° \]

Substituting the value of \( m∠C \):

\[ m∠A + 75° = 180° \]

Now, subtract 75° from both sides:

\[ m∠A = 180° - 75° = 105° \]

Thus, the measure of angle A is

\[ \boxed{105°} \]