In Fig. 6.16, if AB || CD, then
(a) ∠2 = ∠3
(b) ∠1 = ∠4
(c) ∠4 = ∠1 + ∠2
(d) ∠1 + ∠2 = ∠3 + ∠4

Solution:

Given, AB || CD

We have to find the correct option.

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

So, ∠BAC = ∠ACD

From the figure,

∠1 = ∠3

Considering triangle ABC,

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.

By exterior angle property,

The interior angles are ∠1 and ∠2.

Therefore, ∠3 + ∠4 = ∠1 + ∠2

✦ Try This: ∠A + ∠B = 64° and ∠A + ∠C = 120°. Calculate each angle of the triangle

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 39

In Fig. 6.16, if AB || CD, then (a) ∠2 = ∠3, (b) ∠1 = ∠4, (c) ∠4 = ∠1 + ∠2, (d) ∠1 + ∠2 = ∠3 + ∠4

Summary:

In Fig. 6.16, if AB || CD, then ∠3 + ∠4 = ∠1 + ∠2.

☛ Related Questions:

• In ∆ABC, ∠Α = 100°, AD bisects ∠A and AD⊥BC. Then, ∠B is equal to: (a) 80°, (b) 20°, (c) 40°, (d) 30 . . . .
• In ∆ABC, ∠Α = 50°, ∠B = 70° and bisector of ∠C meets AB in D (Fig. 6.17). Measure of ∠ADC is: (a) 50 . . . .
• If for ∆ABC and ∆DEF, the correspondence CAB ↔ EDF gives a congruence, then which of the following i . . . .