In Fig. 5.30, which of the following is true?
a. ∠1 = ∠5
b. ∠4 = ∠8
c. ∠5 = ∠8
d. ∠3 = ∠7

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 true.

From the figure,

Corresponding angles are

∠1 and ∠3

∠2 and ∠4

∠7 and ∠5

∠8 and ∠6

Alternate interior angles are

∠3 and ∠2

∠8 and ∠5

Alternate exterior angles are

∠1 and ∠4

∠7 and ∠6

Co-interior angles are

∠2 and ∠5 and

∠8 and ∠3

If two parallel lines are intersected by a transversal, each pair of alternate interior angles is equal.

So, ∠5 = ∠8

Therefore, option c is true.

✦ Try This: In the given figure, if ∠1 + ∠2 = 100°, then find the measure of ∠4.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5

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NCERT Exemplar Class 7 Maths Chapter 5 Problem 39

In Fig. 5.30, which of the following is true? a. ∠1 = ∠5, b. ∠4 = ∠8, c. ∠5 = ∠8, d. ∠3 = ∠7

Summary:

In Fig. 5.30, ∠5 = ∠8 is true

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☛ Related Questions:

• In Fig. 5.31, PQ||ST. Then, the value of x + y is: a. 125°, b. 135°, c. 145°, d. 120°
• In Fig. 5.32, if PQ||RS and QR||TS, then the value a is: a. 95°, b. 90°, c. 85°, d. 75°
• If the sum of measures of two angles is 90°, then the angles are _________. Fill in the blanks to ma . . . .