Answer:
m∠1 = m∠3 = m∠6 = m∠8 = 31°
m∠2 = m∠4 = m∠5 = m∠7 = 149°
Step-by-step explanation:
From the provided diagram, we can see that ∠1 and ∠5 form a linear pair. This means that they sum to 180°. Given that m∠5 = 149°, we can find m∠1 as follows:
m∠1 + m∠5 = 180°
m∠1 + 149° = 180°
m∠1 = 180° - 149°
m∠1 = 31°
As line t intersects parallel lines w and v, the angles in the same relative positions formed by these intersections are congruent. Therefore, we observe the following congruences:
m∠1 = m∠3
m∠2 = m∠4
m∠5 = m∠7
m∠6 = m∠8
Additionally, when two straight lines intersect, opposite vertical angles are congruent, so:
m∠1 = m∠6
m∠2 = m∠5
m∠3 = m∠8
m∠4 = m∠7
This implies that:
m∠1 = m∠3 = m∠6 = m∠8
m∠2 = m∠4 = m∠5 = m∠7
Given that m∠1 = 31° and m∠5 = 149°, then:
m∠1 = m∠3 = m∠6 = m∠8 = 31°
m∠2 = m∠4 = m∠5 = m∠7 = 149°
