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Question
In the adjoining figure, if line m || line n and line p are a transversal then find x.
Options
135°
90°
45°
40°
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Solution
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°
RELATED QUESTIONS
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`
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(5) ∠s and `square`
(6) ∠w and `square`
Observe the angles shown in the figure and write the following pair of angles.
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A line which intersects two or more lines in different points is known as
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?
Which pair represents alternate interior angles?
If two parallel lines are cut by a transversal, what is the sum of any pair of exterior allied angles ?
