Question 39

In the given figure, if $A B ∥ C D$ , then

a) $∠ 2 = ∠ 3$
b) $∠ 1 = ∠ 4$
c) $∠ 4 = ∠ 1 + ∠ 2$
d) $∠ 1 + ∠ 2 = ∠ 3 + ∠ 4$

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Solution

Given, $A B ∥ C D$ and AC is the transversal.
So, $∠ 1 = ∠ 3$ [alternate interior angles]

Also, in $Δ A B C, ∠ 3 + ∠ 4 = ∠ 1 + ∠ 2$
[ $∵$ exterior angle = sum of two opposite interior angles]

Hence option (d) is correct.

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Question 39 In the given figure, if AB∥CD, then a) ∠2=∠3 b) ∠1=∠4 c) ∠4=∠1+∠2 d) ∠1+∠2=∠3+∠4

Given, AB∥CD and AC is the transversal. So, ∠1=∠3 [alternate interior angles] Also, in ΔABC, ∠3+∠4=∠1+∠2 [∵ exterior angle = sum of two opposite interior angles] Hence option (d) is correct.

Question 39

In the given figure, if $A B ∥ C D$ , then

a) $∠ 2 = ∠ 3$
b) $∠ 1 = ∠ 4$
c) $∠ 4 = ∠ 1 + ∠ 2$
d) $∠ 1 + ∠ 2 = ∠ 3 + ∠ 4$

Given, $A B ∥ C D$ and AC is the transversal.
So, $∠ 1 = ∠ 3$ [alternate interior angles]

Also, in $Δ A B C, ∠ 3 + ∠ 4 = ∠ 1 + ∠ 2$
[ $∵$ exterior angle = sum of two opposite interior angles]

Hence option (d) is correct.