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

Answer:

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, $91^{\circ}$