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

m∠5 = 91°

Explanation:

In the given question a and b, e and f are the parallel lines and ∠1 = 89°.

We have to find the measurement of ∠5.

Since ∠4 = ∠5 (opposite angles)

∠4 = ∠3 (alternate angles)

Therefore ∠5 = ∠3

Since ∠2 = ∠3 (alternate angles)

Therefore ∠5 = ∠2

Since m∠1 + m∠2 = 180°

Therefore m∠1 + m∠5 = 180°

Now we know m∠1 = 89°

89° + m∠5 = 180°

m∠5 = 180° - 89°

m∠5 = 91°

Therefore m∠5 = 91° is the answer.

Answer 2

the picture in the attached figure

we know that
step 1
m∠1+m∠2=180°------> by supplementary angles
m∠2=180°-89°----->m∠2=91°

step 2
m∠4=m∠2------> by corresponding angles
m∠4=91°

step 3
m∠5=m∠4------> by vertical angles
m∠5=91°

the answer is
m∠5=91°