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

75°
75 degrees

15°
15 degrees

105°
105 degrees

180°

Answer 1

When two lines intersect, they create two pairs of vertical angles that are equal to each other, and adjacent angles are supplementary (they add up to 180°).

Given:

• m∠C = 75°
• Angle B is adjacent to angles A and C.

Since angles B and C are adjacent, their measures add up to 180°.

So, we can use the relationship:

m∠B + m∠C = 180°

Substituting the value of m∠C:

m∠B + 75° = 180°

To find m∠B:

m∠B = 180° - 75° = 105°

Now, since angles A and B are vertical angles, m∠A = m∠B:

Thus, m∠A = 105°.

The correct response is:

105°