To solve the problem and to find the missing statement and reason in step 5, let's go through the detailed, step-by-step solution:
1. Given Information:
- \( m \angle ADE = 60^\circ \)
- \( m \angle CDF = (3x + 15)^\circ \)
Reason 1: Given.
2. Identify Vertical Angles:
- \( \angle ADE \) and \( \angle CDF \) are vertical angles.
Reason 2: Definition of vertical angles.
3. Vertical Angles are Equal:
- \( \angle ADE = \angle CDF \)
Reason 3: Vertical angles have equal measures.
4. Equal Measures:
- \( m \angle ADE = m \angle CDF \)
Reason 4: Definition of congruent angles.
5. Substitute the Given Values:
- Substitute the given values into the equation.
- \( 60 = 3x + 15 \)
Reason: Substitution.
6. Solve for \( x \):
- Subtract 15 from both sides:
[tex]\[
60 - 15 = 3x
\][/tex]
[tex]\[
45 = 3x
\][/tex]
Missing Statement and Reason:
- Statement: \( 45 = 3x \),
- Reason: Subtraction property of equality.
7. Solve for \( x \):
- Divide both sides by 3:
[tex]\[
\frac{45}{3} = x
\][/tex]
[tex]\[
x = 15
\][/tex]
Reason: Division property of equality.
So, the missing statement and reason in step 5 are:
Statement: \( 45 = 3x \)
Reason: Subtraction property of equality.
