Answer:
Option 3, m∠8=125∘
Step-by-step explanation:
The answer choices given include:
m∠6=125∘
m∠7=125∘
m∠8=125∘
m∠3=125∘
A few theorems we could use include:
Vertical angles are congruent.
Alternate interior angles are congruent
Same side interior angles are supplementary.
This said, we can go through the options and figure out which ones are true.
∠6 and ∠4 are Same side interior angles and are therefore supplementary.
m∠6 = 180-125 = 55
Option 1 is not true.
∠6 and ∠7 are Vertical angles and are therefore congruent.
We previously ruled that m∠6=55 and therefore m∠7 =55
Option 2 is not true.
We can use ∠5 to see if m∠8=125.
∠5 and ∠4 are Alternate interior angles and therefore are congruent.
∠8 and ∠5 are Vertical angles and are therefore congruent.
Hence, m∠8=125
Option 3 is true.
A line is 180 degrees. ∠3 and ∠4 are supplementary. Therefore, m∠3=55 (180-125)
Option 4 is not true.
