Question

given ( mangle ade = 60^circ ) and ( mangle cdf=(3x + 15)^circ ) prove ( x = 15 ) what is the missing statement and the missing reason in step 5? statements reasons 1 ( mangle ade=60^circ ) ( mangle cdf=(3x + 15)^circ ) 1 given 2 ( angle ade ) and ( angle cdf ) are vert ( angle s ) 2 def of vert ( angle s ) 3 ( angle adecongangle cdf ) 3 vert ( angle scong ) 4 ( mangle ade=mangle cdf ) 4 def of ( cong ) 5? 5? 6 ( 45 = 3x ) 6 subtr prop 7 ( 15=x ) 7 div prop statement ( 60 = 3x+15 ), reason substitution statement ( x = 15 ), reason subtraction property of equality statement ( 60 = 3x + 15 ), reason transitive property statement ( x = 15 ), reason subtraction and division properties of equality

Explanation:

Step1: Recall the given values

We know \(m\angle ADE=60^{\circ}\) (given) and \(m\angle CDF=(3x + 15)^{\circ}\) (given), and from step 4 \(m\angle ADE=m\angle CDF\) (definition of congruent angles).

Step2: Substitute the angle - measures

Substitute \(m\angle ADE = 60\) and \(m\angle CDF=3x + 15\) into the equation \(m\angle ADE=m\angle CDF\). So, by substitution (if \(a = b\) and \(a=c\), then \(c = b\)), we get \(60=3x + 15\).

For the other options:

• Option 2: \(x = 15\) is the result of solving \(60=3x + 15\) (using subtraction and division properties), not a statement for step 5.
• Option 3: The transitive property (\(a=b,b = c\Rightarrow a=c\)) is not applicable here. We are using substitution of known angle - measure values.
• Option 4: \(x = 15\) is the final result after solving the equation \(60=3x+15\) (steps 6 and 7), not for step 5.

Answer:

Statement: \(60 = 3x + 15\), Reason: substitution