A number 5 is quadrupled and then decreased by f

20-f

Step-by-step explanation:

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.