Answer:
m<MON = 100°
Explanation:
Given:
Area of shaded sector LOM = 2π cm²
NL = 6 cm
Required:
m<MON
Solution:
m<MON = 180° - m<LOM (angles in a straight line)
We don't know m<LOM. Therefore, let's find m<LOM.
Area of a sector = θ/360 × πr²
Area of sector LOM = 2π cm²
r = 3 cm
θ = m<LOM = ?
Plug in the values
2π = m<LOM/360 × π × 3²
2π = m<LOM/360 × 9π
2π = m<LOM × 9π/360
2π = m<LOM × π/40
Multiply both sides by 40
2π × 40 = m<LOM × π
80π = m<LOM × π
Divide both sides by π
80π/π = m<LOM
80 = m<LOM
m<LOM = 80°
✔️m<MON = 180° - m<LOM (angles in a straight line)
Substitute
m<MON = 180° - 80°
m<MON = 100°
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