Question

Greg is constructing a fence that consists of parallel sides ed and fb. complete the proof to explain how he can show that m/fac = 121° by finding the missing justifications. statement ed fb mzecg 121° mzecg m2eca = 180° mzfac m2zeca = 180° m/ecg mzeca = m/fac mzeca transitive property subtraction property symmetric property mzecg= m/fac mzfac=mzecg m/fac= -121° justification given linear pair postulate 1. 2. o 1. corresponding angles theorem; 2. definition of supplementary angles o 1. definition of supplementary angles; 2. corresponding angles theorem theorem; 2. substitution property o 1. same-side interior. 1. substitution property: 2. same-side interior angles theorem

Answer 1

Using geometrical properties and postulates including the Linear Pair Postulate and the Corresponding Angles Theorem, it's demonstrated that the angle m/⟩FAC equals 121° in Greg's fence construction scenario due to the parallel nature of the sides.

Step-by-step explanation:

The statements in the question address a geometric scenario where Greg is constructing a fence with parallel sides and needs to establish angle measures. To explain how Greg can show that m/⟩FAC equals 121°, we use a combination of the Linear Pair Postulate, the Corresponding Angles Theorem, and properties to describe the relationships between angles formed when parallel lines are intersected by a transversal. Here are the steps involved in proving that m/⟩FAC equals 121°:

1. Given: ED || FB, m/⟩ZECG = 121°.
2. Linear Pair Postulate: m/⟩ZECG + m/⟩ECA = 180° (because they are a linear pair).
3. Subtraction Property: m/⟩ZECG = m/⟩FAC as they are corresponding angles and lines ED and FB are parallel.
4. Transitive Property: If m/⟩ZECG = 121° and m/⟩ZECG = m/⟩FAC, then m/⟩FAC = 121°.

Summarily, given the parallel nature of lines ED and FB as well as the corresponding angles created, through the use of geometrical properties and postulates, we determine that m/⟩FAC is indeed 121°.