Question

HELP PLEASE

Daniel is constructing a fence that consists of parallel sides line AB and line EF. Complete the proof to explain how he can show that m∠GKB = 120° by filling in the missing justifications.


Statement Justification

line AB ∥ line EF

m∠ELJ = 120° Given

m∠ELJ + m∠ELK = 180° Linear Pair Postulate

m∠BKL + m∠GKB = 180° Linear Pair Postulate

m∠ELJ + m∠ELK = m∠BKL + m∠GKB Transitive Property

∠ELK ≅ ∠BKL 1.

m∠ELK = m∠BKL 2.

m∠ELJ + m∠ELK = m∠ELK + m∠GKB Substitution Property

m∠ELJ = m∠GKB Subtraction Property

m∠GKB = m∠ELJ Symmetric Property

m∠GKB = 120° Substitution

Answer 1

Given that AB and EF have a common transversal, GJ, we have;

• mELK ≈ mBKL, 1. By alternate interior angles theorem

• mELK = mBKL, 2. by definition of congruency

How can the statements that prove mGKB = 120° be found?

Given that AB is parallel to EF, we have;

Line AB || line EF

mELJ = 120° given

mELJ + mELK = mBKL + mGKB; Transitive property of equality

• mELK ≈ mBKL, 1. By alternate interior angles theorem

• mELK = mBKL, 2. by definition of congruency

mELJ + mELK = mELK + mGKB

mELJ = mGKB

mGKB = 120° by substitution property

Learn more about alternate interior angles here:

https://brainly.com/question/15160868