There are angles whose measures add to 180°

Question

. 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

31°
31 degrees

62°
62 degrees

82°

Answer 1

To find the measure of angle B, we have the following angles:

• \( m∠A = 67° \)
• \( m∠B = (2x + 20)° \)
• \( m∠C = x° \)

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

\[ m∠A + m∠B + m∠C = 180° \]

Substituting the expressions we have:

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

Combine the terms:

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

This simplifies to:

\[ 87 + 3x = 180 \]

Now, solve for \( x \):

\[ 3x = 180 - 87 \] \[ 3x = 93 \] \[ x = 31 \]

Now, substitute \( x \) back into the expression for \( m∠B \):

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

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