Question

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

Answer 1

Answer:

∠y=54°, ∠z=126°, ∠x=126°

Step-by-step explanation:

Answer 2

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.