Question

B. Write the correct reasons on each statement.
Prove:
L2 and L7 are supplementary angles
Reasons
Statements
b
2
3. 4
(ML.4)(mL 5) = 180
4 mL 2 = mL4; ML5 = ml?
5. (mL 2)(mL7) = 180
6. L2 and L7 are supplementary
angles​

Answer 1

Given : a || b

To Find :  Show that L2 and L7 are supplementary angles​

Solution:

Properties of angles formed by transversal line  with two parallel lines :

• Corresponding angles are congruent.  

• Alternate angles are congruent.  ( Interiors & Exterior  both )  

• Interior angles are supplementary. ( adds up to 180°)

Statement                             Reason

a ||  b                                       Given

L2 = L4 and L5 = L7               Vertically opposite angles

mL4 + mL5 = 180°                   Interior angles are supplementary

mL2 = mL4 and mL5 = mL7   congruent angles are equal

mL2 + mL7 = 180°                    Substitute mL4  = mL2 and  mL5 = mL7

L2 and L7 are supplementary angles  angles add up to 180°

QED

Hence Proved

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Answer 2

Answer:

Step-by-step expB. Write the correct reasons on each statement.

a

8 7

5 16

43

1\2

b

Given:

a || b

Prove:

L2 and L7 are supplementary

Reasons

angles

Statements

1. a | b

2. L2= L4; 25= L7

3. (mL 4 )(mL 5) = 180

mL 2 = mL4; ml 5= ml

5. (mL 2)(mL 7) = 180

6. L2 and L7 are supplementary

angles

4lanation: