Question

There is a pair of vertical angles whose measures are m∠1=106° and m∠2=(3x−75)° . What equation can you write to solve for x ?(1 point) Responses 3x°−75°−106°=180° 3 x minus 75 minus 106 degrees equals 180 degrees 3x°−75°+106°=180° 3 x minus 75 plus 106 degrees equals 180 degrees 3x°−75°=106° 3 x minus 75 equals 106 degrees 3x°−75°+106°=90°

Answer 1

Since angles ∠1 and ∠2 are vertical angles, they are equal in measure. Therefore, we can set the measures of the angles equal to each other to form an equation.

Given:

• m∠1 = 106°
• m∠2 = (3x - 75)°

We can write the equation as: \( 3x - 75 = 106 \)

This matches the response: 3x - 75 = 106°.

This would be the correct equation to solve for \( x \).