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 1. ( mangle ade = 60^{circ} ) ( mangle cdf=(3x + 15)^{circ} ) 2. ( angle ade ) and ( angle cdf ) are vert. ( angle s ) 3. ( angle adecongangle cdf ) 4. ( mangle ade=mangle cdf ) 5. ? 6. ( 45 = 3x ) 7. ( 15 = x ) reasons 1. given 2. def. of vert. ( angle s ) 3 vert ( angle scong ) 4 def. of 5 ? 6 subtr. prop. 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: Substitute the given angle measures

Since \(m\angle ADE = 60^{\circ}\) (given) and \(m\angle CDF=(3x + 15)^{\circ}\) (given), and \(m\angle ADE=m\angle CDF\) (from step 4: definition of congruent angles). By substitution, we replace \(m\angle ADE\) with \(60\) and \(m\angle CDF\) with \(3x + 15\).

Step2: Analyze the reason

The substitution property of equality states that if \(a=b\) and \(a = c\), then \(b=c\). Here, \(a=m\angle ADE\), \(b = 60\), and \(c=(3x + 15)\).

Answer:

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