In Fig. 5.65, show that EF || GH
Solution:
Given, the figure represents two lines AB and CD cut by the lines EF and GH.
We have to determine if the lines EF and GH are parallel or not.
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°.
From the figure,
∠GKL + ∠LKJ = 180°
∠LKJ + 50° = 180°
∠LKJ = 180° - 50°
∠LKJ = 130°
If two parallel lines are intersected by a transversal, each pair of corresponding angles are equal.
From the figure,
∠LKJ = ∠ALI = 130°
We observe that the corresponding angles are equal.
Therefore, the lines EF and GH are parallel.
✦ Try This: Measures (in degrees) of two complementary angles are consecutive even integers. Find the angles
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 112 (ii)
In Fig. 5.65, show that EF || GH
Summary:
In Fig. 5.65, it is shown that EF || GH.
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