Question

In a hexagon JKLMNO, side JK || ON and ∠K : ∠L : ∠M : ∠N = 6 : 5 : 4 : 3. Find the angle ∠K and ∠M.

Answer 1

Given JK || ON
⇒ ∠J + ∠O = 180°
Also, ∠K : ∠L : ∠M : ∠N = 6 : 5 : 4 : 3
⇒ ∠K = 6x, ∠L = 5x, ∠M = 4x and ∠N = 3x
Since, ∠J + ∠K + ∠L + ∠M +∠N = 4 x 180°
⇒ (∠J + ∠O) +∠K + ∠L + ∠M + ∠N = 4 x 180°
⇒180° + 6x + 5x + 4x + 3x = 720°
⇒ 18x + 180° = 720°
⇒18x = 540°
⇒ x = 30°
Hence,
∠K = 6x
= 6 x 30°
= 180°
and
∠M = 4x
= 4 x 30°
= 120°.