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

82°
82 degrees

180°
180 degrees

62°
62 degrees

31°

Answer 1

To find the measure of ∠B, we will first establish the equation based on the fact that the angles sum to 180°.

Given:

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

According to the problem, we have:

m∠A + m∠B + m∠C = 180°

Substituting the measures of the angles into the equation:

67° + (2x + 20)° + x° = 180°

Now, combine like terms:

67° + 20° + 2x + x = 180° 87° + 3x = 180°

Next, we will isolate x by subtracting 87° from both sides:

3x = 180° - 87° 3x = 93°

Now, divide both sides by 3:

x = 31°

Now we will find m∠B using the value of x:

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

Thus, the measure of ∠B is:

82°.