Question

Here are two intersecting lines.
What is the measure of angle c?
a = 34ºb = 34ºcº
Angle c measures
degrees.

Answer 1

When two lines intersect, the angles opposite each other are called vertical angles, and they are always equal. Since you have angles \( a \) and \( b \) both measuring \( 34^\circ \), angle \( c \), which is adjacent to angle \( b \), can be calculated using the fact that the sum of the angles around a point is \( 360^\circ \) or the adjacent angle property where two adjacent angles sum to \( 180^\circ \).

So if angle \( b \) is \( 34^\circ \), angle \( c \) can be found as follows:

\[
c = 180^\circ - b = 180^\circ - 34^\circ = 146^\circ
\]

Thus, angle \( c \) measures \( 146^\circ \).