Question

AB, CD and EF are three lines intersecting at the same point.
(I) Find x, if y = 45° and z = 90°.
(II) Find a, if x = 3a, y = 5x and z = 6x.​

Answer 1

Answer:

Solution:

AB, CD and EF are intersecting each other at o.

And ∠DOF = x°, ∠AOC = y°

and ∠BOE = z°

But ∠DOB = ∠AOC = y°

(Vertically opposite angles)

Similarly, ∠COE = ∠DOF = x°

And ∠AOF = ∠BOE = z°

∵ CD is a straight line

∴ ∠COE + ∠BOE + ∠DOB = 180°

⇒ x° + z° + y° = 180°

⇒ x° + y° + z° = 180°

(i) If y = 45° and z = 90°, then

⇒ x° + 45° + 90° = 180°

⇒ x° + 135° = 180°

∴ x° = 180° - 135° = 45°

(ii) If x = 3a, y = 5x, z = 6x,

Then x + y + z = 180°

⇒ x + 5x + 6x = 180° ⇒ 12x = 180°

⇒ x = 180°/12 = 15°

But x = 3a

∴ 3a = 15° ⇒ a = 15°/3 = 5°

Hence a = 5°