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

15°
15 degrees

105°
105 degrees

75°

Answer 1

When two lines intersect, they create angles that are related to each other. Angles A and C are opposite angles (also called vertical angles), and angles B and D are also opposite.

Given that \( m∠C = 75° \):

• Because angles A and C are vertical angles, we have \( m∠A = m∠C = 75° \).

Therefore, \[ m∠A = 75° \]

The correct answer is \( 75° \) (75 degrees).