If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles
Solution:
Given, a transversal intersects two parallel lines.
The difference of two interior angles on the same side of a transversal is 20°.
We have to determine the angles.
Consider two parallel lines l and m with P as a transversal,
Let the two interior angles be x and y.
According to the question,
x - y = 20°
So, y = x - 20°
If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.
So, x + y = 180°
x + x - 20° = 180°
2x = 180° + 20°
2x = 200°
x = 200°/2
x = 100°
Now, y = 100° - 20° = 80°
Therefore, the angles are 100° and 80°.
✦ Try This: If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 40°, find the angles.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 96
If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles
Summary:
If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, the angles are 100° and 80°
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