Question

There are angles whose measures add to 180°
. Their measures are: m∠A=67°
, m∠B=(2x+20)°
, and m∠C=x°
. What is the measure of ∠B
?(1 point)
Responses

180°
180 degrees

62°
62 degrees

31°
31 degrees

82°

Answer 1

To find the measure of angle B, we start with the information given:

1. \( m∠A = 67° \)
2. \( m∠B = (2x + 20)° \)
3. \( m∠C = x° \)

Since the angles add up to 180°, we can set up the following equation:

\[
m∠A + m∠B + m∠C = 180°
\]

Substituting the values, the equation becomes:

\[
67° + (2x + 20)° + x° = 180°
\]

Now, combine the terms:

\[
67° + 20° + 2x + x = 180°
\]

This simplifies to:

\[
87° + 3x = 180°
\]

Next, subtract 87° from both sides:

\[
3x = 180° - 87°
\]
\[
3x = 93°
\]

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

\[
x = \frac{93°}{3} = 31°
\]

Now we can find \( m∠B \):

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

Thus, the measure of \( ∠B \) is:

\[
\boxed{82°}
\]