Question

There are angles his measures add to 180° their measures are M angle a = 67° M angle B equals(2X +20) degrees and M angle C equals X degrees what is the measure of angle B?
82°
62°
31°
180°

Answer 1

Given that \( M \angle A + M \angle B + M \angle C = 180° \), we can substitute the values provided:

- \( M \angle A = 67° \)
- \( M \angle B = 2X + 20° \)
- \( M \angle C = X° \)

Now, we can set up the equation:

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

Combining like terms:

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

\[
87 + 3X = 180
\]

Next, we will isolate \( X \):

\[
3X = 180 - 87
\]

\[
3X = 93
\]

\[
X = \frac{93}{3} = 31
\]

Now that we have \( X \), we can find the measure of angle B:

\[
M \angle B = 2X + 20 = 2(31) + 20 = 62 + 20 = 82°
\]

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