Question

Here are two intersecting lines. Angle a measures 135 degrees. Find the measure of angles b and c.
Start by finding the measure of angle b.
a = 135ºbºcº

Angle b measures
135
degrees.
Excellent!
What is the measure of angle c?
a = 135ºb = 135ºcº

Angle c measures
degrees.

Answer 1

When two lines intersect, they create pairs of vertical angles, which are equal to each other.

Given that angle \( a \) measures \( 135^\circ \), we can deduce the measure of angle \( b \), as:

- Angle \( a \) and angle \( b \) are linear pairs, which means they add up to \( 180^\circ \):

\[
b = 180^\circ - a = 180^\circ - 135^\circ = 45^\circ
\]

Now, since angle \( c \) is vertically opposite angle \( b \), it is equal to \( b \):

- Therefore, angle \( c \), which measures the same as angle \( b\), is:

\[
c = 45^\circ
\]

Thus:

- Angle \( b \) measures \( 45^\circ \)
- Angle \( c \) measures \( 45^\circ \)

To clarify:

- Angle \( a = 135^\circ \)
- Angle \( b = 45^\circ \)
- Angle \( c = 45^\circ \)