Question

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

75

15

180

105

Answer 1

When two lines intersect, they create four angles that are related in the following ways:

1. Adjacent angles (those that share a common side) are supplementary, meaning they add up to \(180^\circ\).
2. Opposite angles (those that are across from each other) are equal.

Given that \( m\angle C = 75^\circ \), we can find \( m\angle A \):

Since angles \( A \) and \( C \) are opposite angles, we know that:
\[
m\angle A = m\angle C = 75^\circ
\]

However, angle \( B \) is adjacent to angles \( A \) and \( C \). Therefore, we need to determine \( m\angle B \):
\[
m\angle B + m\angle C = 180^\circ
\]
\[
m\angle B + 75^\circ = 180^\circ
\]
\[
m\angle B = 180^\circ - 75^\circ = 105^\circ
\]

Now, since angle \( D \) is opposite angle \( B \):
\[
m\angle D = m\angle B = 105^\circ
\]

Thus, we conclude:
- \( m\angle A = 75^\circ \)
- \( m\angle B = 105^\circ \)
- \( m\angle C = 75^\circ \)
- \( m\angle D = 105^\circ \)

So the value of \( m\angle A \) is:
\[
\boxed{75}
\]