If two angles have a common vertex and their arms form opposite rays (Fig. 5.41). Then, how many types of angles are formed
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 find how many types of angles are formed.
(i) 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.
(ii) When the sum of the measures of two angles is 180°, the angles are called supplementary angles.
(iii) Adjacent angles are the angles that have a common arm (side) and a common vertex, however, they do not overlap.
A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.
(iv) Linear pairs of angles are formed when two lines intersect each other at a single point.
The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.
Therefore, four types of angles are formed.
✦ Try This: One angle is equal to two 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 (b)
If two angles have a common vertex and their arms form opposite rays (Fig. 5.41). Then, how many types of angles are formed
Summary:
If two angles have a common vertex and their arms form opposite rays (Fig. 5.41). Then, 4 types of angles are formed
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