Question

Lines A and b are parallel and lines e and f are parallel. If m<1=89, what is the measure of <5?

M<5=?

Answer 1

if < 1 = 89, the < 5 = 91

Answer 2

Given the statement:

Lines a and b are parallel and lines e and f are parallel.

if
`m \angle 1 = 89^(\circ)`

By supplementary angles:

`m\angle 1+ m\angle 2 = 180^(\circ)`

⇒
`89^(\circ)+ m\angle 2 = 180^(\circ)`

Subtract 89 degree from both sides we have;

`m \angle 2 = 91^(\circ)`

Since,

m∠4 = m∠5 [Vertically Opposite angles] .....[1]

m∠4 = m∠3 [Alternate Interior angle] .....[2]

By [1] and [2] we have;

m∠5 =m∠3 ....[3]

Also;

m∠2 = m∠3 [Alternate interior angle] ....[4]

by [3] and [4] we have;

m∠5 = m∠2

Substitute the given values we have;

`m \angle 5 = 91^(\circ)`

Therefore, the measure of
`m \angle 5` is,
`91^(\circ)`