Question

In the above figure, ∠L = 35°, find :

1. m(arc MN)
2. m(arc MLN)

Solution :

1. ∠L = `1/2` m(arc MN) ............(By inscribed angle theorem)
   ∴ `square = 1/2` m(arc MN)
   ∴ 2 × 35 = m(arc MN)
   ∴ m(arc MN) = `square`
2. m(arc MLN) = `square` – m(arc MN) ...........[Definition of measure of arc]
   = 360° – 70°
   ∴ m(arc MLN) = `square`

Answer 1

1. ∠L = `1/2` m(arc MN) ............(By inscribed angle theorem)
   ∴ 35° = `1/2` m(arc MN)
   ∴ 2 × 35 = m(arc MN)
   ∴ m(arc MN) = 70°
2. m(arc MLN) = 360° – m(arc MN) ...........[Definition of measure of arc]
   = 360° – 70°
   ∴ m(arc MLN) = 290°