Question

Two intersecting lines create four angles with the same vertex labels a,b,c, and d. Angle b is adjacent angle a and angle c find measure of angle a is measure of angle c is 75

Answer 1

In the scenario you provided, where two intersecting lines create four angles labeled \( a \), \( b \), \( c \), and \( d \), we can use the properties of adjacent angles and vertical angles to find the measure of angle \( a \).

Given:
- \( \text{measure of angle } c = 75^\circ \)
- Angles \( a \) and \( c \) are vertical angles.
- Angles \( a \) and \( b \) are adjacent angles.

Since angle \( c \) is \( 75^\circ \), angle \( a \), being vertical to angle \( c \), will also measure \( 75^\circ \).

Adjacent angles \( a \) and \( b \) sum to \( 180^\circ \):

\[
\text{measure of angle } a + \text{measure of angle } b = 180^\circ
\]

Substituting the measure of angle \( a \):

\[
75^\circ + \text{measure of angle } b = 180^\circ
\]

To find the measure of angle \( b \):

\[
\text{measure of angle } b = 180^\circ - 75^\circ = 105^\circ
\]

Now, we can summarize:
- \( \text{measure of angle } a = 75^\circ \)
- \( \text{measure of angle } b = 105^\circ \)
- \( \text{measure of angle } c = 75^\circ \)
- \( \text{measure of angle } d = 105^\circ \) (since \( d \) is vertical to \( b \))

In conclusion, the measure of angle \( a \) is \( 75^\circ \).