Answer:
m∠2 is 55°
Step-by-step explanation:
Let us revise some facts in geometry
- In any triangle, the sum of the measures of its angles is 180°
- If two line intersected at a point, then they formed two pairs of vertically opposite angles, the vertically opposite angles are equal in measures
We will use these facts to solve our question
∵ ∠1 is an angle of a triangle
∴ m∠1 + 40° + 85° = 180° ⇒ 1st fact
→ Add the like terms in the left side
∴ m∠1 + 125° = 180°
→ Subtract 125° from both sides
∴ m∠1 + 125° - 125° = 180° - 125°
∴ m∠1 = 55°
∵ ∠1 and ∠2 formed from the intersecting of two lines
∴ ∠1 and ∠2 are vertically opposite angles
∴ m∠1 = m∠2 ⇒ 2nd fact
∵ m∠1 = 55°
∴ m∠2 = 55°
