Question

Huge help needed ! im lost and need an explanation to the correct answer.

Answer 1

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°