Question

given: m∠ade = 60° and m∠cdf=(3x + 15)° prove: x = 15 what is the missing statement and the missing reason in step 5? statements reasons 1. m∠ade = 60° m∠cdf=(3x + 15)° 1. given 2. ∠ade and ∠cdf are vert. ∠s 2. def. of vert. ∠s 3. ∠ade≅∠cdf 3. vert. ∠s≅ 4. m∠ade = m∠cdf 4. def. of ≅ 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 previous statements

We know from statement 1 that $m\angle ADE = 60^{\circ}$ and from statement 4 that $m\angle ADE=m\angle CDF$.

Step2: Substitute the values

By the substitution property, if $m\angle ADE = 60^{\circ}$ and $m\angle ADE=m\angle CDF$, then $60 = 3x + 15$.

Answer:

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