In Fig. 5.30, which one of the following is not true?
a. ∠1 + ∠5 = 180°
b. ∠2 + ∠5 = 180°
c. ∠3 + ∠8 = 180°
d. ∠2 + ∠3 = 180°
Solution:
Given, the figure represents a line l intersects two parallel lines PQ and RS.
We have to determine which of the given options is false.
From the properties of angles formed by transversal on two parallel lines,
If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.
From the figure,
The consecutive interior angles are 2 and 5.
By the property,
∠2 + ∠5 = 180° -------------------------- (1)
Therefore, option b is true.
Similarly, ∠3 + ∠8 = 180° ------------- (2)
Therefore, option c is true.
We know that vertically opposite angles are equal.
From the figure,
∠1 = ∠2 ----------------------------- (3)
From (1) and (3),
∠1 + ∠5 = 180°
Therefore, option a is true.
Considering ∠2 + ∠3 = 180°,
From the figure,
We observe that angle 2 and 3 are alternate interior angles.
The sum of alternate interior angles is greater than 180°.
So, ∠2 + ∠3 ≠ 180°
Therefore, option d is false.
✦ Try This: In the figure, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 38
In Fig. 5.30, which one of the following is not true? a. ∠1 + ∠5 = 180°, b. ∠2 + ∠5 = 180°, c. ∠3 + ∠8 = 180°, d. ∠2 + ∠3 = 180°
Summary:
In Fig. 5.30, ∠2 + ∠3 = 180° is not true
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