In Fig. 5.63, examine whether the following pairs of lines are parallel or not: EF and GH
Solution:
Given, the figure represents two lines EF and GH cut by two lines AB and CD.
We have to determine if the lines EF and GH are parallel or not.
Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
Vertically opposite angles are equal to each other.
From the figure,
∠x = 65°
Considering lines EF and GH cut by the line CD,
Linear pairs of angles are formed when two lines intersect each other at a single point.
Linear pair angles are supplementary angles as their sum is 180°.
So, 70° + y = 180°
y = 180° - 70°
y = 110°
If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.
Now, x + y = 65° + 110°
= 175° ≠ 180°
The sum of co interior angles is not equal to 180 degrees.
Therefore, the lines EF and GH are not parallel.
✦ Try This: In the figure, two parallel lines l and m are cut by two transversal p and q. Find the values of x.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 110 (i)
In Fig. 5.63, examine whether the following pairs of lines are parallel or not: EF and GH
Summary:
In Fig. 5.63, the lines EF and GH are not parallel.
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