If two angles have a common vertex and their arms form opposite rays (Fig. 5.41). Then, write all the pairs of vertically opposite angles
Solution:
Given, the figure represents two lines AC and BD which intersect at O.
Two angles have a common vertex and their arms form opposite rays.
We have to write all the pairs of vertically opposite angles.
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,
The vertically opposite angles are
∠1 and ∠3
∠2 and ∠4
Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
By the above theorem,
∠1 = ∠3
∠2 = ∠4
Therefore, the vertically opposite angles are ∠1, ∠3 and ∠2, ∠4.
✦ Try This: One angle is equal to four times its supplement. The measure of the angle is
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 81 (c)
If two angles have a common vertex and their arms form opposite rays (Fig. 5.41). Then, write all the pairs of vertically opposite angles
Summary:
If two angles have a common vertex and their arms form opposite rays (Fig. 5.41). Then, all the pairs of vertically opposite angles are ∠1, ∠3 and ∠2, ∠4.
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