In Fig. 5.30, line l intersects two parallel lines PQ and RS. Then, which one of the following is not true?
a. ∠1 = ∠3
b. ∠2 = ∠4
c. ∠6 = ∠7
d. ∠4 = ∠8
Solution:
Given, the line l intersects two parallel lines PQ and RS.
We have to determine which of the given options is false.
Considering ∠1 = ∠3,
If two parallel lines are intersected by a transversal, each pair of corresponding angles are equal.
From the above property,
The corresponding angles 1 and 3 are equal
Therefore, option a is true
Considering ∠2 = ∠4
If two parallel lines are intersected by a transversal, each pair of corresponding angles is equal.
From the above property,
The corresponding angles 2 and 4 are equal
Therefore, option b is true
Considering ∠6 = ∠7,
We know that the vertically opposite angles are equal.
From the figure,
Angle 6 and 7 are vertically opposite
Therefore, option c is true.
Considering ∠4 = ∠8,
We know that the sum of a linear pair of angles is always equal to 180 degrees.
∠2 + ∠8 = 180°
We know, ∠2 = ∠4
So, ∠4 + ∠8 = 180°
∠4 ≠ ∠8
Therefore, option d is false.
✦ Try This: Find all the pairs of vertically opposite angles.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 37
In Fig. 5.30, line l intersects two parallel lines PQ and RS. Then, which one of the following is not true? a. ∠1 = ∠3, b. ∠2 = ∠4, c. ∠6 = ∠7, d. ∠4 = ∠8
Summary:
In Fig. 5.30, line l intersects two parallel lines PQ and RS. Then, ∠4 = ∠8 is not true
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