Missy is constructing a fence that consists of parallel sides line AB and line EF. Complete the proof to explain how she can show that m∠AKL = 116° by filling in the missing justifications. Statement Justification line AB ∥ line EF m∠KLF = 116° Given m∠KLF+ m∠BKL = 180° 1. m∠BKL + m∠AKL = 180° Linear Pair Postulate m∠KLF + m∠BKL = m∠BKL + m∠AKL 2. m∠KLF = m∠AKL Subtraction Property m∠AKL = m∠KLF Symmetric Property m∠AKL = 116° Substitution Property A. 1. Alternate Interior Angles Theorem; 2. Substitution Property B. 1. Definition of Complementary Angles; 2. Substitution Property C. 1. Definition of Supplementary Angles; 2. Transitive Property D. 1. Same-Side Interior Angles Theorem; 2. Transitive Property

The correct option is;

D. 1. Same-Side Interior Angles Theorem

2. Transitive Property

Step-by-step explanation:

The two column proof is given as follows;

Statement                                                Justification

line AB║line EF                                         Given

m∠KLF = 116°                                              Given

1. m∠KLF + m∠BKL = 180                          1. Same side supplementary angles

2. m∠BKL + m∠AKL = 180°                         Linear pair postulate

3. m∠KLF + m∠BKL = m∠BKL + m∠AKL    2. Transitive property

4. m∠KLF = m∠AKL                                    Subtraction property      

5. m∠AKL = m∠KLF                                     Symmetric property

6. m∠AKL = 116°                                           Substitution property.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.