Question

There are angles whose measures add to 180. Their measures are: m<A = 67, m<B = ( 2x + 20 ) and m<C = x. Wut is da measure of <B?

82

180

31

62

Answer 1

The angles \( A \), \( B \), and \( C \) are supplementary, meaning they add up to 180 degrees. We know:

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

First, we can set up the equation based on the angle measures:

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

Substituting the values we have:

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

Now, combine like terms:

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

\[
87 + 3x = 180
\]

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

\[
3x = 180 - 87
\]

\[
3x = 93
\]

Now, divide by 3:

\[
x = 31
\]

Now that we have \( x \), we can find \( m<B \):

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

\[
m<B = 62 + 20 = 82
\]

Thus, the measure of angle \( B \) is \(\boxed{82}\).