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 = 16); reason: subtraction property of equality statement: (60 = 3x + 15); reason: transitive property statement: (x = 15); reason: subtraction and division properties of equality

Explanation:

Step1: Use angle - equality

Since $\angle ADE$ and $\angle CDF$ are vertical angles and $\angle ADE = 60^{\circ}$, $\angle CDF=(3x + 15)^{\circ}$, and vertical angles are equal, we have $m\angle ADE=m\angle CDF$. Substituting the given angle - measures, we get the equation $60 = 3x+15$.

Step2: Apply subtraction property

Subtract 15 from both sides of the equation $60 = 3x + 15$. So, $60-15=3x+15 - 15$, which simplifies to $45 = 3x$.

Step3: Apply division property

Divide both sides of the equation $45 = 3x$ by 3. So, $\frac{45}{3}=\frac{3x}{3}$, which gives $x = 15$.

Answer:

Statement: $60 = 3x + 15$; Reason: substitution