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 vertical - angle property

Vertical angles are equal. Given $\angle ADE$ and $\angle CDF$ are vertical angles, so $m\angle ADE=m\angle CDF$. Since $m\angle ADE = 60^{\circ}$ and $m\angle CDF=(3x + 15)^{\circ}$, we substitute the values.

Step2: Identify the substitution step

We substitute the measures of the angles into the equality $m\angle ADE=m\angle CDF$. So the statement is $60 = 3x+15$ and the reason is substitution property.

Answer:

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