Question

if m<1 =89, what is the measure of <5?

Answer 1

<5 would be at the same position as the angle under <1. 

So, <5 and <1 are adjacent and equal to 180 degrees.

180-89= 91

<5 equals 91 degrees. 

I hope this helps!
~kaikers

Answer 2

Answer:

The measure of ∠5 is 91°.

Step-by-step explanation:

Since, By the given diagram,

∠1 and ∠2 are linear pairs,

So, by the property of linear pairs,

∠1 + ∠2 = 180°

Given, ∠1 = 89°,

⇒ 89° + ∠2 = 180°

⇒ ∠2 = 180° - 89° = 91°,

Now, a ║ b ( given ),

By the alternate interior angle theorem,

∠2 = ∠3

⇒ ∠3 = 91°

Also, e ║ f ( given )

Again by the alternate interior angle theorem,

∠3 = ∠4

⇒ ∠4 = 91° ,

Finally by the diagram,

∠4 and ∠5 are vertically opposite angles,

⇒ ∠4 = ∠5

⇒ ∠5 = 91°