Question

Here are two intersecting lines. Angle a measures 154 degrees. Find the measure of angles b and c.
Start by finding the measure of angle b.
a = 154ºbºcº

Angle b measures
degrees.

Answer 1

When two lines intersect, they create pairs of vertical angles, and the angles on a straight line add up to 180 degrees.

Given that angle \( a \) measures \( 154^\circ \), we can find angle \( b \) using the fact that angles \( a \) and \( b \) are supplementary (they form a straight line).

To find angle \( b \):
\[
b = 180^\circ - a
\]
\[
b = 180^\circ - 154^\circ = 26^\circ
\]

So, angle \( b \) measures \( 26^\circ \).

Now, let's find angle \( c \). Angles \( b \) and \( c \) are also vertical angles, which means they are equal:
\[
c = b
\]
Thus:
\[
c = 26^\circ
\]

In summary:
- Angle \( a = 154^\circ \)
- Angle \( b = 26^\circ \)
- Angle \( c = 26^\circ \)

Therefore, angle \( b \) measures \( 26 \) degrees.