Question

in given figure line AB,CD and EF intersecting at O. Find the value of x,y and z it is being given that x:y:z=2:3:5​

Answer 1

Answer:

X = 36°, y = 54°, z = 90°

The ratio of the values of ∠x, ∠y, and ∠z = 2:3:5

Let the angles be 2a, 3a, and 5a

∠BOF = ∠AOE = x°  = 2a (Alternete angles)

∠EOD = ∠COF = y° = 3a (Alternate angles)

∠AOC = ∠DOB = z° = 5a (Alternete angles)

∵ ∠EOD + ∠DOB + ∠BOF + ∠FOC + ∠COA + ∠AOE = 360°

3a + 5a + 2a + 3a + 5a + 2a = 360°

20a = 360°

a = 360/20 = 18°

∵ x = 2a = 2 * 18 = 36°

y = 3a = 3 * 18 = 54°

z = 5a = 5 * 18 = 90°

Therefore, x = 36° , y = 54° , and z = 90°