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° given m∠cdf=(3x + 15)° 2. ∠ade and ∠cdf are vert. ∠s def. of vert. ∠s 3. ∠ade≅∠cdf vert. ∠s≅ 4. m∠ade = m∠cdf def. of ≅ 5. ? 5. ? 6. 45 = 3x subtr. prop 7. 15 = x div prop. statement: 60 = 3x + 15; reason: substitution statement: x = 15; reason: subtraction property of equality statement: 60 ≠ 3x + 15; reason: subtraction property statement: x = 15; reason: substitution and division properties of equality

Explanation:

Step1: Recall vertical - angle property

We know that vertical angles are equal. Given $\angle ADE$ and $\angle CDF$ are vertical angles, and $m\angle ADE = 60^{\circ}$, $m\angle CDF=(3x + 15)^{\circ}$.

Step2: Substitute values

Since $m\angle ADE=m\angle CDF$ (by the definition of congruent vertical angles), we substitute the given angle - measures. So, $60 = 3x+15$ by the substitution property.

Answer:

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