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°=90° 3 x minus 75 plus 106 degrees equals 90 degrees 3x°−75°=106° 3 x minus 75 equals 106 degrees 3x°−75°+106°=180° 3 x minus 75 plus 106 degrees equals 180 degrees 3x°−75°−106°=180°
The correct equation to solve for x is: 3x - 75 = 106
Together, the measures of ∠B , ∠C , and ∠D equal 180° . The angles have the following measures: m∠B=25° , m∠C=(3x)° , and m∠D=(3x+5)° . What are the measures of ∠C and ∠D ?
To find the measures of ∠C and ∠D, we need to solve the equation: m∠B + m∠C + m∠D = 180°
Given that m∠B = 25°, m∠C = 3x°, and m∠D = 3x + 5°, we can substitute these values into the equation:
25 + 3x + (3x + 5) = 180
Simplifying the expression, we get:
25 + 3x + 3x + 5 = 180
Combine like terms:
6x + 30 = 180
Subtract 30 from both sides:
6x = 150
Divide both sides by 6:
x = 25
Now we can substitute x back into the expressions for ∠C and ∠D:
m∠C = 3(25) = 75°
m∠D = 3(25) + 5 = 80°
Therefore, ∠C measures 75° and ∠D measures 80°.