Answer:
10) m∠2 = 139°
11) m∠3 = 139°
12) m∠4 = 41°
Explanation:
Question 10
∠2 and the adjacent angle of 41° are supplementary angles since they lie on opposite sides of the same line; they must add up to 180°
m∠2 + 41° = 180°
m∠2 = 180-41 =139°
Question 11
∠2 and ∠3 are formed by the intersection of two rays. They are vertically opposite angles and therefore they must be equal
m∠3 = m∠2 = 139°
Question 12
Angles ∠3 and ∠4 are supplementary angles (same reasoning as q 10)
Therefore m∠4 = 180° - m∠3
= 180° - 139° = 41°
Note that there are many ways to arrive at the answers for m∠4
- angles 4 and 41° are opposite vertical angles so they must be equal and m∠4 = 41°
- angles 2 and 4 are supplementary and therefore m∠2 + m∠4 = 180° => 139 + m∠4 = 180° or m∠4 = 180 - 139 = 41°