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प्रश्न
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 r = 6x.
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उत्तर
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 + ∠DOE = 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°
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