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प्रश्न
In the adjoining figure, if line m || line n and line p are a transversal then find x.
विकल्प
135°
90°
45°
40°
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उत्तर
45°
Explanation:
Let us mark P and Q on m, R, and S on n, A, and B on p.
Suppose PQ and AB intersect at M; RS and AB intersect at N.
Since, m||n and p are transversals, then
m∠QMN + m∠SNM = 180° (Interior angles on the same side of transversal are supplementary)
Substituting the values in the above equation, we get
3x + x = 180°
⇒ 4x = 180°
⇒ x = `(180°)/4`
∴ x = 45°
संबंधित प्रश्न
In the adjoining figure, identify:
- The pairs of corresponding angles.
- The pairs of alternate interior angles.
- The pairs of interior angles on the same side of the transversal.
- The vertically opposite angles.
In the adjoining figure, each angle is shown by a letter. Fill in the boxes with the help of the figure.
Corresponding angles.
(1) ∠p and `square`
(2) ∠q and `square`
(3) ∠r and `square`
(4) ∠ s and `square`
Interior alternate angles.
(5) ∠s and `square`
(6) ∠w and `square`
Observe the angles shown in the figure and write the following pair of angles.
Interior alternate angles
Observe the angles shown in the figure and write the following pair of angles.
Corresponding angles
In the adjoining figure, if line a || line b and line l is a transversal then find x.
A transversal intersects two or more than two lines at ______ points.
If two parallel lines are intersected by a transversal, what is the relationship between the corresponding angles formed?
When a transversal intersects two parallel lines, what is the sum of any pair of consecutive interior angles?
A line is defined as a transversal if it satisfies which of the following conditions?
If two parallel lines are cut by a transversal, what is the sum of any pair of exterior allied angles ?
