In a pair of adjacent angles,
(i) vertex is always common,
(ii) one arm is always common, and
(iii) uncommon arms are always opposite rays Then
a. All (i), (ii) and (iii) are true
b. (iii) is false
c. (i) is false but (ii) and (iii) are true
d. (ii) is false
Solution:
Given, a pair of adjacent angles
(i) vertex is always common,
(ii) one arm is always common, and
(iii) uncommon arms are always opposite rays
We have to determine the suitable options.
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.
From the properties of adjacent angles, we know that
a. Adjacent angles always share a common arm.
b. They have a non-common arm on both sides of the common arm.
From the above definition,
It is clear that adjacent angles have common vertex and a common arm
But uncommon arms are not always opposite rays.
Therefore, (i), (ii) are true and (iii) is false.
✦ Try This: In the given figure write each pair of vertically opposite angles.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 29
In a pair of adjacent angles, (i) vertex is always common, (ii) one arm is always common, and (iii) uncommon arms are always opposite rays Then, a. All (i), (ii) and (iii) are true, b. (iii) is false, c. (i) is false but (ii) and (iii) are true, d. (ii) is false
Summary:
In a pair of adjacent angles, (i) vertex is always common, (ii) one arm is always common, and (iii) uncommon arms are always opposite rays. Then (iii) is false
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