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

62°
62 degrees

180°
180 degrees

31°
31 degrees

82°

Answer 1

To find the measure of angle \( \angle B \), we start with the information that the sum of the angles is 180°. We are given:

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

Since the sum of the angles is 180°, we can set up the equation:

\[ 67° + (2x + 20)° + x° = 180° \]

Simplifying this equation:

\[ 67 + 2x + 20 + x = 180 \] \[ 87 + 3x = 180 \]

Now, subtract 87 from both sides:

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

Now, divide by 3:

\[ x = 31 \]

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

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

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