Question

Find the value of x, y and z

Answer 1

∠DOB and ∠BOC are linear pair

∴ ∠DOB + ∠BOC = 180°

x + 3x + 40 = 180°

4x + 40 = 180°

4x + 40 – 40 = 180° – 40°

4x = 140°

x = `(140^circ)/4`

x = 35°

Also ∠BOD and ∠AOC are vertically opposite angles.

∴ ∠BOD = ∠AOC

x = z + 10

35° = z + 10

z + 10 – 10 = 35 – 10

z = 25°

Again ∠AOD and ∠AOC are linear pair.

∴ ∠AOD + ∠AOC = 180°

y + 30 + z + 10 = 180°

y + 30 + 25 + 10 = 180°

y + 65 = 180°

y + 65 – 65 = 180° – 65

y = 115°

∴ x = 35°,

y = 115°,

z = 25°