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

82°
82 degrees

31°

Answer 1

To find the measure of ∠B, we need to set up an equation based on the given information about the angles. The problem states that:

\[
m∠A + m∠B + m∠C = 180°
\]

Given:
- \( m∠A = 67° \)
- \( m∠B = (2x + 20)° \)
- \( m∠C = x° \)

Now we can substitute these values into the equation:

\[
67° + (2x + 20)° + x° = 180°
\]

Combining like terms:

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

This simplifies to:

\[
3x + 87 = 180
\]

Now, subtract 87 from both sides:

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

Now, divide by 3:

\[
x = 31
\]

Now that we have \( x \), we can find the measure of \( m∠B \):

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

Thus, the measure of \( ∠B \) is:

\[
\boxed{82°}
\]