Question

In the given figure, if AB is parallel to CD, L2= 120° + x and L6 = 6x. Find the measure of L2 and L6.​

Answer 1

Answer:

The measure of ∠2 = 144° and ∠6 = 144°.

Step-by-step explanation:

Given : AB is parallel to CD.

∠2 = 120° + x, ∠6 = 6x.

To find: The measures of ∠2 and ∠6.

Solution :

Since, AB ║CD, ∠2 and ∠6 are corresponding angles and so they are equal.

(When a transversal intersects two parallel lines , then the pair of corresponding angles are equal.)

so, ∠2 = ∠6 .Here, ∠2 = 120° + x and ∠6 = 6x.

Now, 120° + x = 6x

     ⇒ 120 = 6x -x

     ⇒ 5x = 120.

     ⇒ x = 120 ÷ 5 = 24.

Then, substituting x=24 in ∠2 and ∠6we get,

∠2 = 120° + x = 120° + 24 = 144°, and

 ∠6 = 6x = 6 × 24 = 144° .

∴ The measure of ∠2 = 144° and ∠6 = 144°.

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Answer 2

Answer:

The measure of ∠2 = 144° and ∠6 = 144°.

Step-by-step explanation:

Step 1 of 2

Given: AB is parallel to CD and PQ is the transversal line.

∠2 = 120° + x and ∠6 = 6x

From the figure,

Observe that the ∠2 and ∠6 are the corresponding angles.

As we know, the pair of corresponding angles are equal when a transversal cuts the pair of parallel lines.

⇒ ∠2 = ∠6

⇒ 120° + x = 6x

⇒ 120° = 6x - x

⇒ 120° = 5x

⇒ x = 24°

Step 2 of 2

Find the measure of ∠2 and ∠6.

(i) Since ∠2 = 120° + x

⇒ ∠2 = 120° + 24°

⇒ ∠2 = 144°

(ii) Since ∠6 = 6x

⇒ ∠6 = 6(24)

⇒ ∠6 = 144°

Final answer: The measure of ∠2 = 144° and ∠6 = 144°.

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