50 - 100 1. provide reasons for the proof. given: line p is parallel to line r. prove: ∠1 is supplementary to ∠7.

step-by-step explanation:

given : line p is parallel to line r

to prove : ∠1 is supplementary to ∠7

proof :

1) line p is parallel to line r (given)

∠2=∠3 ( corresponding angles of parallel lines are equal)

∠3=∠7 ( vertically opposite angles are equal)

∴ ∠2 ≅ ∠7

2) ∠2 ≅ ∠7 ( from above reason i.e. corresponding angles and vertically opposite angles )

⇒ m∠2=m∠7

3) m∠2=m∠7 ( equal angles have equal measures)

4) since ∠1 and ∠2 forms a linear pair as there is a line cut by transversal because of which   ∠1 and ∠2 forms a linear pair

⇒ ∠1 is supplementary to ∠2.

5) ∠1 is supplementary to ∠2. ( ∵ ∠1 and ∠2 forms a linear pair.)

6)

reason :   ∠1 is supplementary to ∠2.

now, we use m∠2=m∠7 in the above equation,

so it becomes,

7)

reason: by substituting ∠2=∠7

⇒ ∠1 is supplementary to ∠7.

8) ∠1 is supplementary to ∠7 (∵ )

hence proved.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.