Math, asked by kirt32, 1 year ago

in figure if AB//CD,CD//EF and y:z=3:7,find x​

Answers

Answered by sameercjali
17

Answer:

∠y=54°, ∠z=126°, ∠x=126°

Step-by-step explanation:

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Answered by silentlover45
30

Figure:-

Given:-

  • AB // CD and CD // EF
  • Y : Z = 3 : 7

To find:-

  • find the x ...?

Solutions:-

AB // CD and CD // EF (lines parallel to the same line are parallel to the each other)

It can be observed that.

x = z ⠀⠀⠀⠀⠀⠀⠀⠀(Alternate interior angle)......(i).

y : z = 3 : 7

Let the common ratio between y and z be a.

y = 3a and z = 7a

Also,

⟹ x + y = 180°. (co - interior angle on the same side of the transversal).

⟹ z + y = 180°. ⠀⠀⠀⠀⠀⠀[using equation (i)]

⟹ 7a + 3a = 180°

⟹ 10a = 180°

⟹ a = 180°/10

⟹ a = 18°

  • x = 7a = 7 × 18° = 126°
  • 7a = 7 × 18° = 126°
  • 3a = 3 × 18° = 54°

Additional Information:-

  • Straight line = Angle which measures 180°.
  • Supplementary Angle = The two angle are supplementary, if there sum are 90°.
  • Complementary Angle = The two angle are complementary, if these sum are 90°.

Some Important:-

A transversal intersects two parallel lines.

  • The corresponding angles are equal.
  • The vertically opposite angles are equal.
  • The alternate interior angles are equal.
  • The alternate exterior angles are equal.
  • The pair of interior angles on the same side of the transversal is supplementary.
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