in figure if AB//CD,CD//EF and y:z=3:7,find x
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Answered by
17
Answer:
∠y=54°, ∠z=126°, ∠x=126°
Step-by-step explanation:
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Answered by
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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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