For Fig. 5.20, statements p and q are given below:
p : a and b are forming a linear pair.
q : a and b are forming a pair of adjacent angles.
Then,
a. both p and q are true
b. p is true and q is false
c. p is false and q is true
d. both p and q are false
Solution:
Given, the statements a and b.
We need to find which of the above statements satisfy the given options.
Considering statement p,
We know that the sum of all angles lying on a straight line is equal to 180 degrees.
The linear pair of angles is always equal to 180 degrees.
From the figure,
a + b = 180°
a and b form a linear pair of angles.
Therefore, the statement p is true.
Considering statement q,
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 figure,
O is a point on the line AB
So, ∠AOC and ∠BOC have common vertex and common arm
∠AOC and ∠BOC are adjacent angles
Therefore, the statement q is true.
✦ Try This: In the given figure, write down each pair of corresponding angles.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 24
For Fig. 5.20, statements p and q are given below: p : a and b are forming a linear pair. q : a and b are forming a pair of adjacent angles. Then, a. both p and q are true, b. p is true and q is false, c. p is false and q is true, d. both p and q are false
Summary:
For Fig. 5.20, statements p and q are given below:
p : a and b are forming a linear pair.
q : a and b are forming a pair of adjacent angles. Both the statements p and q are true
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