Question

There are angles whose measures add to 180 . their measure are: m<A = 67 , m<B = (2x + 20) , and m<C = x . what is the measure of <B? (1 point)
A. 180
B. 31
C. 62
D. 82

Answer 1

To find the measure of angle \( B \), we first set up the equation based on the information given. The angles \( A \), \( B \), and \( C \) are supplementary, meaning their measures add up to 180 degrees:

\[
m<A + m<B + m<C = 180
\]

Given:

- \( m<A = 67 \)
- \( m<B = 2x + 20 \)
- \( m<C = x \)

Substituting these values into the equation gives us:

\[
67 + (2x + 20) + x = 180
\]

Now, combine like terms:

\[
67 + 20 + 3x = 180
\]
\[
87 + 3x = 180
\]

Next, we isolate \( 3x \) by subtracting 87 from both sides:

\[
3x = 180 - 87
\]
\[
3x = 93
\]

Now, divide by 3 to find \( x \):

\[
x = 31
\]

Now we can substitute \( x \) back to find the measure of angle \( B \):

\[
m<B = 2x + 20 = 2(31) + 20 = 62 + 20 = 82
\]

Thus, the measure of angle \( B \) is:

\[
\boxed{82}
\]